Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80401	Find the Derivative - d/dx	d/(dx)(arcsin(e^(5x)))	$\frac{d}{d x} (\arcsin (e^{5 x}))$
80402	Evaluate the Integral	integral of (-3x-3)/( square root of x^2+2x-4) with respect to x	$\int \frac{- 3 x - 3}{\sqrt{x^{2} + 2 x - 4}} d x$
80403	Evaluate the Integral	integral of 2e^(x+5) with respect to x	$\int 2 e^{x + 5} d x$
80404	Find Where Increasing/Decreasing	-x^4+8x^3-18x^2	$- x^{4} + 8 x^{3} - 18 x^{2}$
80405	Find the Antiderivative	g(x)=x^2+2x-1	$g (x) = x^{2} + 2 x - 1$
80406	Find the Maximum/Minimum Value	f(x)=-x^3+3x^2-3x+1	$f (x) = - x^{3} + 3 x^{2} - 3 x + 1$
80407	Find the Antiderivative	3x^2sin(x^3+2003)	$3 x^{2} \sin (x^{3} + 2003)$
80408	Find the Antiderivative	cube root of 2x	$\sqrt[3]{2 x}$
80409	Evaluate the Integral	integral of (x^2+1)^3x^3 with respect to x	$\int {(x^{2} + 1)}^{3} x^{3} d x$
80410	Evaluate the Integral	integral from pi/3 to (2pi)/3 of csc(1/2t)^2 with respect to t	$\int_{\frac{π}{3}}^{\frac{2 π}{3}} \csc^{2} (\frac{1}{2} t) d t$
80411	Find the Antiderivative	f(x)=1/(x^3)+2	$f (x) = \frac{1}{x^{3}} + 2$
80412	Evaluate the Integral	integral from 0 to 1 of arctan(2x) with respect to x	$\int_{0}^{1} \arctan (2 x) d x$
80413	Find the Antiderivative	f(x)=1/(cos(x)^2)	$f (x) = \frac{1}{\cos^{2} (x)}$
80414	Find the Derivative - d/dx	d/(dx)(arcsin(e^(3x)))	$\frac{d}{d x} (\arcsin (e^{3 x}))$
80415	Find dy/dx	-xy+x=-4	$- x y + x = - 4$
80416	Evaluate from the Left	limit as x approaches 1 of x^2-2x+4	$lim_{x \to 1} x^{2} - 2 x + 4$
80417	Find the Antiderivative	x square root of x-3/( square root of x)	$x \sqrt{x} - \frac{3}{\sqrt{x}}$
80418	Find the Antiderivative	f(x)=tan(x)sec(x)^2	$f (x) = \tan (x) \sec^{2} (x)$
80419	Find the Antiderivative	-1/(x^2)	$\frac{- 1}{x^{2}}$
80420	Evaluate the Limit	limit as x approaches 0 of (1-cos(2x))/(xsin(x))	$lim_{x \to 0} \frac{1 - \cos (2 x)}{x \sin (x)}$
80421	Evaluate the Limit	limit as x approaches 0 of (sin(2x^2)+tan(2x)^2)/(3x^2)	$lim_{x \to 0} \frac{\sin (2 x^{2}) + \tan^{2} (2 x)}{3 x^{2}}$
80422	Find the Antiderivative	x/(e^x)	$\frac{x}{e^{x}}$
80423	Find the Derivative - d/dx	-3x^(1/3)	$- 3 x^{\frac{1}{3}}$
80424	Find Where Increasing/Decreasing	f(x)=x^4+x^2-2	$f (x) = x^{4} + x^{2} - 2$
80425	Find the Antiderivative	(x^2)/( square root of x^3+1)	$\frac{x^{2}}{\sqrt{x^{3} + 1}}$
80426	Evaluate the Integral	integral from 0 to pi of integral from 0 to 2pi of cos(theta)sin(theta)sin(x)^2(sin(x)-sin(theta)) with respect to theta with respect to x	$\int_{0}^{π} \int_{0}^{2 π} \cos (θ) \sin (θ) \sin^{2} (x) (\sin (x) - \sin (θ)) d θ d x$
80427	Find the Derivative - d/dx	2(sin(x))/(cos(x))+2cot(x)*sin(x)	$2 \frac{\sin (x)}{\cos (x)} + 2 \cot (x) \cdot \sin (x)$
80428	Find the Antiderivative	27x^2+cos(x)	$27 x^{2} + \cos (x)$
80429	Evaluate the Summation	sum from i=1 to 11 of 3i^2-8	$\sum_{i = 1}^{11} 3 i^{2} - 8$
80430	Evaluate the Integral	integral of ((3x-2)^2)/( square root of x) with respect to x	$\int \frac{{(3 x - 2)}^{2}}{\sqrt{x}} d x$
80431	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(tan(3x))	$lim_{x \to 0} \frac{\sin (x)}{\tan (3 x)}$
80432	Find the Derivative - d/dx	y=3^4*x^3	$y = 3^{4} \cdot x^{3}$
80433	Evaluate the Limit	limit as x approaches 0 from the right of x natural log of x+x^2	$lim_{x \to 0^{+}} x \ln (x + x^{2})$
80434	Evaluate the Limit	limit as x approaches 16 of ( fourth root of x^7-128)/(x-16)	$lim_{x \to 16} \frac{\sqrt[4]{x^{7}} - 128}{x - 16}$
80435	Integrate By Parts	integral of e^(2theta)sin(2theta) with respect to theta	$\int e^{2 θ} \sin (2 θ) d θ$
80436	Evaluate Using Summation Formulas	sum from k=1 to n of k/(n^2)	$\sum_{k = 1}^{n} \frac{k}{n^{2}}$
80437	Find the Derivative - d/dx	7^( square root of x+2)	$7^{\sqrt{x} + 2}$
80438	Evaluate the Limit	limit as x approaches -8 of -(4(x+5)^2+1)/(1/(3x+2)+2)	$lim_{x \to - 8} - \frac{4 {(x + 5)}^{2} + 1}{\frac{1}{3 x + 2} + 2}$
80439	Find the Antiderivative	e^x+x	$e^{x} + x$
80440	Evaluate the Integral	integral of (7x+e^(4x)) with respect to x	$\int (7 x + e^{4 x}) d x$
80441	Find the Antiderivative	cube root of x-2	$\sqrt[3]{x - 2}$
80442	Evaluate the Limit	limit as x approaches infinity of (-2x^3-2x+3)/(3x^3+3x^2-5x)	$lim_{x \to \infty} \frac{- 2 x^{3} - 2 x + 3}{3 x^{3} + 3 x^{2} - 5 x}$
80443	Evaluate the Integral	integral from -2 to 4 of (x/2+3) with respect to x	$\int_{- 2}^{4} (\frac{x}{2} + 3) d x$
80444	Find the Second Derivative	y=7x^3-5x^2+x	$y = 7 x^{3} - 5 x^{2} + x$
80445	Find the Antiderivative	2/(x^2-1)	$\frac{2}{x^{2} - 1}$
80446	Evaluate the Integral	integral of (8x-3)/((4x^2-3x)^4) with respect to x	$\int \frac{8 x - 3}{{(4 x^{2} - 3 x)}^{4}} d x$
80447	Find Where Increasing/Decreasing	2x^4-16x^3+36x^2	$2 x^{4} - 16 x^{3} + 36 x^{2}$
80448	Evaluate the Limit	limit as x approaches 0 of 2/((sin(x))/x)+(1-cos(x))/x+(tan(x))/x	$lim_{x \to 0} \frac{2}{\frac{\sin (x)}{x}} + \frac{1 - \cos (x)}{x} + \frac{\tan (x)}{x}$
80449	Find the Percentage Rate of Change	f(x)=0.75(0.1)^x	$f (x) = 0.75 {(0.1)}^{x}$
80450	Find Where Increasing/Decreasing	f(x)=e^(x^2-1)	$f (x) = e^{x^{2} - 1}$
80451	Evaluate the Integral	integral of 3(5+x)^2 with respect to x	$\int 3 {(5 + x)}^{2} d x$
80452	Evaluate the Integral	integral of (x-5)^2e^x with respect to x	$\int {(x - 5)}^{2} e^{x} d x$
80453	Integrate Using u-Substitution	integral of 2x square root of x-5 with respect to x	$\int 2 x \sqrt{x - 5} d x$
80454	Find the Derivative - d/dt	y=(2t-3)/(t+2)	$y = \frac{2 t - 3}{t + 2}$
80455	Evaluate the Limit	limit as x approaches 6 of square root of (x^2-9)/(x-3)	$lim_{x \to 6} \sqrt{\frac{x^{2} - 9}{x - 3}}$
80456	Integrate Using u-Substitution	integral from 5 to 8 of 1/(x square root of x^2-16) with respect to x	$\int_{5}^{8} \frac{1}{x \sqrt{x^{2} - 16}} d x$
80457	Find the Antiderivative	(x^3)/(x^4+1)	$\frac{x^{3}}{x^{4} + 1}$
80458	Find the Concavity	f(x)=x+3(x-1)^(1/3)	$f (x) = x + 3 {(x - 1)}^{\frac{1}{3}}$
80459	Find the Linearization at θ=0	f(theta)=cos(theta+pi/3) about theta=0	$f (θ) = \cos (θ + \frac{π}{3})$ about $θ = 0$
80460	Evaluate the Integral	integral from 0 to x of (1+2t+3t^2+4t^3) with respect to t	$\int_{0}^{x} (1 + 2 t + 3 t^{2} + 4 t^{3}) d t$
80461	Find the Concavity	f(x)=x^5+5x^4	$f (x) = x^{5} + 5 x^{4}$
80462	Find the Derivative - d/dx	(x-1/x)^2	${(x - \frac{1}{x})}^{2}$
80463	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-sin(2x))^(1/(3x))	$lim_{x \to 0} {(1 - \sin (2 x))}^{\frac{1}{3 x}}$
80464	Find the Volume	y=xe^(x^2) , y=-2x , x=1 , x=0	$y = x e^{x^{2}}$ , $y = - 2 x$ , $x = 1$ , $x = 0$
80465	Find the Antiderivative	(x^4+2)/(x^2)	$\frac{x^{4} + 2}{x^{2}}$
80466	Evaluate the Integral	integral from 0 to square root of 3 of 6x square root of 1+x^2 with respect to x	$\int_{0}^{\sqrt{3}} 6 x \sqrt{1 + x^{2}} d x$
80467	Find dy/dx	x^2y^2-2xy+x^2=1	$x^{2} y^{2} - 2 x y + x^{2} = 1$
80468	Find the Derivative - d/dx	j (x)=((x^2+1)/(x+2))^3	$j$ $(x) = {(\frac{x^{2} + 1}{x + 2})}^{3}$
80469	Find the Center and Radius	x^2+y^2+50=0	$x^{2} + y^{2} + 50 = 0$
80470	Evaluate the Integral	integral of (e^(cos(x)))(sin(x)) with respect to x	$\int (e^{\cos (x)}) (\sin (x)) d x$
80471	Find the Percentage Rate of Change	r(t)=0.4(1.06)^t	$r (t) = 0.4 {(1.06)}^{t}$
80472	Find the Antiderivative	(e^x)^2	${(e^{x})}^{2}$
80473	Evaluate the Summation	sum from n=1 to infinity of (3n^5)/(15n^4+5)	$\sum_{n = 1}^{\infty} \frac{3 n^{5}}{15 n^{4} + 5}$
80474	Find the Antiderivative	sin(x)^2*cos(x)^2	$\sin^{2} (x) \cdot \cos^{2} (x)$
80475	Evaluate the Limit	limit as x approaches 0 of (sin(pi\|x\|))/(4x)	$lim_{x \to 0} \frac{\sin (π \| x \|)}{4 x}$
80476	Evaluate the Limit	limit as x approaches -1 of -(9x^2-5x-4)(x^(1/3)-2)	$lim_{x \to - 1} - (9 x^{2} - 5 x - 4) (x^{\frac{1}{3}} - 2)$
80477	Find the Antiderivative	(x^3)/(x^2+1)	$\frac{x^{3}}{x^{2} + 1}$
80478	Find dy/dx	y=(5x-1)^(1/3)	$y = {(5 x - 1)}^{\frac{1}{3}}$
80479	Evaluate the Limit	limit as x approaches infinity of (5x^2+2x-5x^4)/(5x^2-2x+1)	$lim_{x \to \infty} \frac{5 x^{2} + 2 x - 5 x^{4}}{5 x^{2} - 2 x + 1}$
80480	Find the Antiderivative	1/(x^2-5x+6)	$\frac{1}{x^{2} - 5 x + 6}$
80481	Evaluate the Summation	sum from n=1 to infinity of (3n^4)/(15n^4+5)	$\sum_{n = 1}^{\infty} \frac{3 n^{4}}{15 n^{4} + 5}$
80482	Find the Inflection Points	f(x)=1/10x^5-12x^3	$f (x) = \frac{1}{10} x^{5} - 12 x^{3}$
80483	Evaluate the Limit	limit as x approaches 0 of (x^2+x)/(x^3+x)	$lim_{x \to 0} \frac{x^{2} + x}{x^{3} + x}$
80484	Evaluate the Integral	integral from -1 to 2 of (\|x\|)/x with respect to x	$\int_{- 1}^{2} \frac{\| x \|}{x} d x$
80485	Find the Maximum/Minimum Value	3cos(x+pi/6)	$3 \cos (x + \frac{π}{6})$
80486	Find the Antiderivative	f(x)=-3/(x^2)+4/(x^3)	$f (x) = - \frac{3}{x^{2}} + \frac{4}{x^{3}}$
80487	Find the Tangent Line at x=-2	f(x)=3x^2+4x at x=-2	$f (x) = 3 x^{2} + 4 x$ at $x = - 2$
80488	Find the Antiderivative	1/((2x-1)^2)	$\frac{1}{{(2 x - 1)}^{2}}$
80489	Evaluate the Integral	integral of (5+x) with respect to x	$\int (5 + x) d x$
80490	Find the Inflection Points	f(x)=1/3x^6+x^5+5/6x^4	$f (x) = \frac{1}{3} x^{6} + x^{5} + \frac{5}{6} x^{4}$
80491	Evaluate the Integral	integral of (-100y^4)/5 with respect to y	$\int \frac{- 100 y^{4}}{5} d y$
80492	Find the Antiderivative	5*2x	$5 \cdot 2 x$
80493	Evaluate the Limit	limit as x approaches infinity of (6x^3-3x)/(x^3+4x^2)	$lim_{x \to \infty} \frac{6 x^{3} - 3 x}{x^{3} + 4 x^{2}}$
80494	Evaluate the Limit	limit as x approaches infinity of (x+1)/( square root of x^2)	$lim_{x \to \infty} \frac{x + 1}{\sqrt{x^{2}}}$
80495	Find the Antiderivative	(x^2-x+1)/(x-1)	$\frac{x^{2} - x + 1}{x - 1}$
80496	Evaluate the Integral	integral of (e^x+e) with respect to x	$\int (e^{x} + e) d x$
80497	Find the Derivative - d/dx	y=(2x)(x+5)	$y = (2 x) (x + 5)$
80498	Integrate Using u-Substitution	integral from 0 to 1 of x square root of 1-x^2 with respect to x	$\int_{0}^{1} x \sqrt{1 - x^{2}} d x$
80499	Evaluate the Summation	sum from k=5 to 5 of (k+1)^2(k-3)	$\sum_{k = 5}^{5} {(k + 1)}^{2} (k - 3)$
80500	Find the Second Derivative	y=(3x^2-6x+1)^2	$y = {(3 x^{2} - 6 x + 1)}^{2}$