Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
85401	Integrate Using u-Substitution	integral of x(x+1)^3 with respect to x	$\int x {(x + 1)}^{3} d x$
85402	Integrate Using u-Substitution	integral of 3x^2(x^3+1)^6 with respect to x	$\int 3 x^{2} {(x^{3} + 1)}^{6} d x$
85403	Integrate Using u-Substitution	integral of sin(2x)cos(2x) with respect to x	$\int \sin (2 x) \cos (2 x) d x$
85404	Integrate Using u-Substitution	integral of 1/(4+x^2) with respect to x	$\int \frac{1}{4 + x^{2}} d x$
85405	Integrate Using u-Substitution	integral of (e^x-e^(-x))/(e^x+e^(-x)) with respect to x	$\int \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} d x$
85406	Integrate Using u-Substitution	integral of (sin( natural log of x))/x with respect to x	$\int \frac{\sin (\ln (x))}{x} d x$
85407	Integrate Using u-Substitution	integral of x(x^2+1)^2 with respect to x	$\int x {(x^{2} + 1)}^{2} d x$
85408	Integrate Using u-Substitution	integral from 1 to e of ( natural log of x)/x with respect to x	$\int_{1}^{e} \frac{\ln (x)}{x} d x$
85409	Integrate Using u-Substitution	integral from 0 to 2 of x square root of 1+2x^2 with respect to x	$\int_{0}^{2} x \sqrt{1 + 2 x^{2}} d x$
85410	Integrate Using u-Substitution	integral from 1 to 2 of (e^(1/x))/(x^2) with respect to x	$\int_{1}^{2} \frac{e^{\frac{1}{x}}}{x^{2}} d x$
85411	Integrate Using u-Substitution	integral of sin(3x) with respect to x	$\int \sin (3 x) d x$
85412	Integrate Using u-Substitution	integral of (x^2)/( square root of 9-x^2) with respect to x	$\int \frac{x^{2}}{\sqrt{9 - x^{2}}} d x$
85413	Integrate Using u-Substitution	integral of 1/( square root of 2x) with respect to x	$\int \frac{1}{\sqrt{2 x}} d x$
85414	Integrate Using u-Substitution	integral of xe^(-x) with respect to x	$\int x e^{- x} d x$
85415	Integrate Using u-Substitution	integral from 0 to 1/4 of (8x)/( square root of 1-4x^2) with respect to x	$\int_{0}^{\frac{1}{4}} \frac{8 x}{\sqrt{1 - 4 x^{2}}} d x$
85416	Integrate Using u-Substitution	integral of tan(x)^2 with respect to x	$\int \tan^{2} (x) d x$
85417	Integrate Using u-Substitution	integral from 0 to pi/6 of (sin(t))/(cos(t)^2) with respect to t	$\int_{0}^{\frac{π}{6}} \frac{\sin (t)}{\cos^{2} (t)} d t$
85418	Integrate Using u-Substitution	integral of (x^2-9)^3(2x) with respect to x	$\int {(x^{2} - 9)}^{3} (2 x) d x$
85419	Integrate Using u-Substitution	integral of 8x square root of 1-x^2 with respect to x	$\int 8 x \sqrt{1 - x^{2}} d x$
85420	Integrate Using u-Substitution	integral of (arctan(x))/(1+x^2) with respect to x	$\int \frac{\arctan (x)}{1 + x^{2}} d x$
85421	Integrate Using u-Substitution	integral of 1/( square root of 1-4x^2) with respect to x	$\int \frac{1}{\sqrt{1 - 4 x^{2}}} d x$
85422	Integrate Using u-Substitution	integral of x^4+x^3-x^2+x-1 with respect to x	$\int x^{4} + x^{3} - x^{2} + x - 1 d x$
85423	Integrate Using u-Substitution	integral of x/( square root of x+1) with respect to x	$\int \frac{x}{\sqrt{x + 1}} d x$
85424	Integrate Using u-Substitution	integral of (1+cos(3x)) with respect to x	$\int (1 + \cos (3 x)) d x$
85425	Integrate Using u-Substitution	integral of xsin(x) with respect to x	$\int x \sin (x) d x$
85426	Integrate Using u-Substitution	integral of -20/( square root of 25-7x^2) with respect to x	$\int \frac{- 20}{\sqrt{25 - 7 x^{2}}} d x$
85427	Integrate Using u-Substitution	integral of (sin(x))/(cos(x)^2) with respect to x	$\int \frac{\sin (x)}{\cos^{2} (x)} d x$
85428	Integrate Using u-Substitution	integral of sin(5x) with respect to x	$\int \sin (5 x) d x$
85429	Integrate Using u-Substitution	integral of x^2 square root of x-1 with respect to x	$\int x^{2} \sqrt{x - 1} d x$
85430	Integrate Using u-Substitution	integral from 0 to pi/6 of sec(2x)tan(2x) with respect to x	$\int_{0}^{\frac{π}{6}} \sec (2 x) \tan (2 x) d x$
85431	Integrate Using u-Substitution	integral of sec(2x)tan(2x) with respect to x	$\int \sec (2 x) \tan (2 x) d x$
85432	Integrate Using u-Substitution	integral of square root of 4-x^2 with respect to x	$\int \sqrt{4 - x^{2}} d x$
85433	Integrate Using u-Substitution	integral of (1+6x)^4(6) with respect to x	$\int {(1 + 6 x)}^{4} (6) d x$
85434	Integrate Using u-Substitution	integral of x(x^2-1)^3 with respect to x	$\int x {(x^{2} - 1)}^{3} d x$
85435	Integrate Using u-Substitution	integral from 0 to 2 of x/((1+2x^2)^2) with respect to x	$\int_{0}^{2} \frac{x}{{(1 + 2 x^{2})}^{2}} d x$
85436	Integrate Using u-Substitution	integral of (e^(1/x))/(x^2) with respect to x	$\int \frac{e^{\frac{1}{x}}}{x^{2}} d x$
85437	Integrate Using u-Substitution	integral from -1 to 1 of x(x^2+1)^3 with respect to x	$\int_{- 1}^{1} x {(x^{2} + 1)}^{3} d x$
85438	Integrate Using u-Substitution	integral of (3y-1) square root of 3y^2-2y with respect to y	$\int (3 y - 1) \sqrt{3 y^{2} - 2 y} d y$
85439	Integrate Using u-Substitution	integral of x/(x+1) with respect to x	$\int \frac{x}{x + 1} d x$
85440	Integrate Using u-Substitution	integral from 0 to pi of sec(x/3)^2 with respect to x	$\int_{0}^{π} \sec^{2} (\frac{x}{3}) d x$
85441	Integrate Using u-Substitution	integral of x^3 square root of 1+x^2 with respect to x	$\int x^{3} \sqrt{1 + x^{2}} d x$
85442	Integrate Using u-Substitution	integral of square root of x with respect to x	$\int \sqrt{x} d x$
85443	Integrate Using u-Substitution	integral of cos(2x) with respect to x	$\int \cos (2 x) d x$
85444	Integrate Using u-Substitution	integral of x(5x^2+4)^3 with respect to x	$\int x {(5 x^{2} + 4)}^{3} d x$
85445	Integrate Using u-Substitution	integral of cos(theta)^3sin(theta) with respect to theta	$\int \cos^{3} (θ) \sin (θ) d θ$
85446	Integrate Using u-Substitution	integral of 2xe^(x^2) with respect to x	$\int 2 x e^{x^{2}} d x$
85447	Integrate Using u-Substitution	integral from 1 to 2 of 2x^2 square root of x^3+1 with respect to x	$\int_{1}^{2} 2 x^{2} \sqrt{x^{3} + 1} d x$
85448	Integrate Using u-Substitution	integral from 0 to 2 of (3x^2-1)/(x^2) with respect to x	$\int_{0}^{2} \frac{3 x^{2} - 1}{x^{2}} d x$
85449	Integrate Using u-Substitution	integral from 0 to 1 of xe^(-x^2) with respect to x	$\int_{0}^{1} x e^{- x^{2}} d x$
85450	Integrate Using u-Substitution	integral of xe^(x^2) with respect to x	$\int x e^{x^{2}} d x$
85451	Integrate Using u-Substitution	integral of xcos(5x^2) with respect to x	$\int x \cos (5 x^{2}) d x$
85452	Integrate Using u-Substitution	integral of 1/(x(1+x^2)) with respect to x	$\int \frac{1}{x (1 + x^{2})} d x$
85453	Integrate Using u-Substitution	integral of x^3 square root of 4-x^2 with respect to x	$\int x^{3} \sqrt{4 - x^{2}} d x$
85454	Integrate Using u-Substitution	integral of (csc(x)^2)/(cot(x)^3) with respect to x	$\int \frac{\csc^{2} (x)}{\cot^{3} (x)} d x$
85455	Integrate Using u-Substitution	integral of (3-2x)^5 with respect to x	$\int {(3 - 2 x)}^{5} d x$
85456	Integrate Using u-Substitution	integral of pisin(pix) with respect to x	$\int π \sin (π x) d x$
85457	Integrate Using u-Substitution	integral of x^2 square root of x+1 with respect to x	$\int x^{2} \sqrt{x + 1} d x$
85458	Integrate Using u-Substitution	integral of (2x+1) square root of x-5 with respect to x	$\int (2 x + 1) \sqrt{x - 5} d x$
85459	Integrate Using u-Substitution	integral from 0 to pi/4 of (sin(t))/(cos(t)^2) with respect to t	$\int_{0}^{\frac{π}{4}} \frac{\sin (t)}{\cos^{2} (t)} d t$
85460	Integrate Using u-Substitution	integral of ( natural log of x)/x with respect to x	$\int \frac{\ln (x)}{x} d x$
85461	Integrate Using u-Substitution	integral from 0 to pi/3 of sin(x)cos(x)^3 with respect to x	$\int_{0}^{\frac{π}{3}} \sin (x) \cos^{3} (x) d x$
85462	Integrate Using u-Substitution	integral of sec(x)^2tan(x)^2 with respect to x	$\int \sec^{2} (x) \tan^{2} (x) d x$
85463	Integrate Using u-Substitution	integral of 1/(x^3) with respect to x	$\int \frac{1}{x^{3}} d x$
85464	Integrate Using u-Substitution	integral of x^2(2x^3-1)^4 with respect to x	$\int x^{2} {(2 x^{3} - 1)}^{4} d x$
85465	Integrate Using u-Substitution	integral from 1 to 3 of (x+1)e^(x^2+2x) with respect to x	$\int_{1}^{3} (x + 1) e^{x^{2} + 2 x} d x$
85466	Integrate Using u-Substitution	integral from 5 to 8 of 1/(x square root of x^2-16) with respect to x	$\int_{5}^{8} \frac{1}{x \sqrt{x^{2} - 16}} d x$
85467	Integrate Using u-Substitution	integral from 0 to 3 of square root of y+1 with respect to y	$\int_{0}^{3} \sqrt{y + 1} d y$
85468	Integrate Using u-Substitution	integral from 1 to e of (( natural log of x)^2)/x with respect to x	$\int_{1}^{e} \frac{\ln^{2} (x)}{x} d x$
85469	Integrate Using u-Substitution	integral of 2x square root of x-5 with respect to x	$\int 2 x \sqrt{x - 5} d x$
85470	Integrate Using u-Substitution	integral from 0 to 1 of cube root of 1+7x with respect to x	$\int_{0}^{1} \sqrt[3]{1 + 7 x} d x$
85471	Integrate Using u-Substitution	integral of (x^3)/(1+x^8) with respect to x	$\int \frac{x^{3}}{1 + x^{8}} d x$
85472	Integrate Using u-Substitution	integral of 1/((1-6t)^4) with respect to t	$\int \frac{1}{{(1 - 6 t)}^{4}} d t$
85473	Integrate Using u-Substitution	integral of (3x^4-5)^5*36x^3 with respect to x	$\int {(3 x^{4} - 5)}^{5} \cdot 36 x^{3} d x$
85474	Integrate Using u-Substitution	integral of xe^(3x) with respect to x	$\int x e^{3 x} d x$
85475	Integrate Using u-Substitution	integral from 0 to 5 of square root of y+4 with respect to y	$\int_{0}^{5} \sqrt{y + 4} d y$
85476	Integrate Using u-Substitution	integral of cot(x)^2 with respect to x	$\int \cot^{2} (x) d x$
85477	Integrate Using u-Substitution	integral of 1/(1+x^2) with respect to x	$\int \frac{1}{1 + x^{2}} d x$
85478	Integrate Using u-Substitution	integral of square root of 9-x^2 with respect to x	$\int \sqrt{9 - x^{2}} d x$
85479	Integrate Using u-Substitution	integral of sin(theta)^2cos(theta) with respect to theta , u=sin(theta)	$\int \sin^{2} (θ) \cos (θ) d θ$ , $u = \sin (θ)$
85480	Integrate Using u-Substitution	integral from 0 to pi/4 of sin(4x) with respect to x	$\int_{0}^{\frac{π}{4}} \sin (4 x) d x$
85481	Integrate Using u-Substitution	integral of (5x+4)^5 with respect to x	$\int {(5 x + 4)}^{5} d x$
85482	Integrate Using u-Substitution	integral of (x^3)/( square root of 1+x^4) with respect to x	$\int \frac{x^{3}}{\sqrt{1 + x^{4}}} d x$
85483	Integrate Using u-Substitution	integral of 7x^3-15x+10 with respect to x	$\int 7 x^{3} - 15 x + 10 d x$
85484	Integrate Using u-Substitution	integral of sin(theta)^4cos(theta) with respect to theta , u=sin(theta)	$\int \sin^{4} (θ) \cos (θ) d θ$ , $u = \sin (θ)$
85485	Integrate Using u-Substitution	integral of (x^2+1)^2 with respect to x	$\int {(x^{2} + 1)}^{2} d x$
85486	Integrate Using u-Substitution	integral of square root of 1-4x with respect to x	$\int \sqrt{1 - 4 x} d x$
85487	Integrate Using u-Substitution	integral of x/( square root of 1-x^4) with respect to x	$\int \frac{x}{\sqrt{1 - x^{4}}} d x$
85488	Integrate Using u-Substitution	integral from 0 to pi/2 of cos((2x)/3) with respect to x	$\int_{0}^{\frac{π}{2}} \cos (\frac{2 x}{3}) d x$
85489	Integrate Using u-Substitution	integral of tan(x)^3 with respect to x	$\int \tan^{3} (x) d x$
85490	Integrate Using u-Substitution	integral of 1/( square root of x) with respect to x	$\int \frac{1}{\sqrt{x}} d x$
85491	Integrate Using u-Substitution	integral from natural log of 2 to natural log of 8 of (e^x)/(1+e^x) with respect to x	$\int_{\ln (2)}^{\ln (8)} \frac{e^{x}}{1 + e^{x}} d x$
85492	Integrate Using u-Substitution	integral from 0 to 3 of x square root of 9-x^2 with respect to x	$\int_{0}^{3} x \sqrt{9 - x^{2}} d x$
85493	Integrate Using u-Substitution	integral of x square root of 1+x with respect to x	$\int x \sqrt{1 + x} d x$
85494	Integrate Using u-Substitution	integral of 1/((8x-1)^3) with respect to x	$\int \frac{1}{{(8 x - 1)}^{3}} d x$
85495	Integrate Using u-Substitution	integral of (sin(x))/(1+cos(x)^2) with respect to x	$\int \frac{\sin (x)}{1 + \cos^{2} (x)} d x$
85496	Integrate Using u-Substitution	integral of e^(cos(x))sin(x) with respect to x	$\int e^{\cos (x)} \sin (x) d x$
85497	Integrate Using u-Substitution	integral of e^(sin(x))cos(x) with respect to x	$\int e^{\sin (x)} \cos (x) d x$
85498	Integrate Using u-Substitution	integral from 1 to 2 of (e^(1/(x^4)))/(x^5) with respect to x	$\int_{1}^{2} \frac{e^{\frac{1}{x^{4}}}}{x^{5}} d x$
85499	Integrate Using u-Substitution	integral of x^3 square root of x^2-1 with respect to x	$\int x^{3} \sqrt{x^{2} - 1} d x$
85500	Integrate Using u-Substitution	integral of (( natural log of x)^5)/x with respect to x	$\int \frac{\ln^{5} (x)}{x} d x$