Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
3601	Evaluate the Integral	integral from 0 to pi/2 of cos((2x)/3) with respect to x	$\int_{0}^{\frac{π}{2}} \cos (\frac{2 x}{3}) d x$
3602	Evaluate the Integral	integral from 0 to pi/2 of sin(x)^5 with respect to x	$\int_{0}^{\frac{π}{2}} \sin^{5} (x) d x$
3603	Evaluate the Integral	integral from 0 to pi/2 of cos(x)^5 with respect to x	$\int_{0}^{\frac{π}{2}} \cos^{5} (x) d x$
3604	Evaluate the Integral	integral of xe^(x/3) with respect to x	$\int x e^{\frac{x}{3}} d x$
3605	Evaluate the Integral	integral of xe^(8x) with respect to x	$\int x e^{8 x} d x$
3606	Evaluate the Integral	integral of ye^y with respect to y	$\int y e^{y} d y$
3607	Evaluate the Integral	integral of 3e^(3x) with respect to x	$\int 3 e^{3 x} d x$
3608	Evaluate the Integral	integral of 3x^2e^(x^3) with respect to x	$\int 3 x^{2} e^{x^{3}} d x$
3609	Evaluate the Integral	integral of 3x^3 with respect to x	$\int 3 x^{3} d x$
3610	Evaluate the Integral	integral of 3xe^(5x) with respect to x	$\int 3 x e^{5 x} d x$
3611	Evaluate the Integral	integral of 3cos(x) with respect to x	$\int 3 \cos (x) d x$
3612	Evaluate the Integral	integral from -4 to 2 of x^2+2x-8 with respect to x	$\int_{- 4}^{2} x^{2} + 2 x - 8 d x$
3613	Evaluate the Integral	integral of 2sec(x)^2 with respect to x	$\int 2 \sec^{2} (x) d x$
3614	Evaluate the Integral	integral of 2sin(x)^2 with respect to x	$\int 2 \sin^{2} (x) d x$
3615	Evaluate the Integral	integral of 2e^(-3x) with respect to x	$\int 2 e^{- 3 x} d x$
3616	Evaluate the Integral	integral of 2(2x+4)^5 with respect to x	$\int 2 {(2 x + 4)}^{5} d x$
3617	Evaluate the Integral	integral of 2cos(x)^2 with respect to x	$\int 2 \cos^{2} (x) d x$
3618	Evaluate the Integral	integral from 2 to 4 of x^2-6x+9 with respect to x	$\int_{2}^{4} x^{2} - 6 x + 9 d x$
3619	Evaluate the Integral	integral from -3 to -2 of 2x(4-x^2)^3 with respect to x	$\int_{- 3}^{- 2} 2 x {(4 - x^{2})}^{3} d x$
3620	Evaluate the Integral	integral from -3 to 2 of x^2+x-6 with respect to x	$\int_{- 3}^{2} x^{2} + x - 6 d x$
3621	Evaluate the Integral	integral of 2 natural log of x with respect to x	$\int 2 \ln (x) d x$
3622	Evaluate the Integral	integral of 20t^3e^(-t^4) with respect to t	$\int 20 t^{3} e^{- t^{4}} d t$
3623	Evaluate the Integral	integral from 24 to 25 of x square root of x^2-576 with respect to x	$\int_{24}^{25} x \sqrt{x^{2} - 576} d x$
3624	Evaluate the Integral	integral of -24x^5 with respect to x	$\int - 24 x^{5} d x$
3625	Evaluate the Integral	integral of 25-x^2 with respect to x	$\int 25 - x^{2} d x$
3626	Evaluate the Integral	integral of 7x^-4 with respect to x	$\int 7 x^{- 4} d x$
3627	Evaluate the Integral	integral of 7xe^(5x^2) with respect to x	$\int 7 x e^{5 x^{2}} d x$
3628	Evaluate the Integral	integral of -7t^-1 with respect to t	$\int - 7 t^{- 1} d t$
3629	Evaluate the Integral	integral from -6 to 7 of x with respect to x	$\int_{- 6}^{7} x d x$
3630	Evaluate the Integral	integral of 6x^3 with respect to x	$\int 6 x^{3} d x$
3631	Evaluate the Integral	integral of 5sin(x) with respect to x	$\int 5 \sin (x) d x$
3632	Evaluate the Integral	integral of 5x cube root of 1-x^2 with respect to x	$\int 5 x \sqrt[3]{1 - x^{2}} d x$
3633	Evaluate the Integral	integral of 5e^(-2x) with respect to x	$\int 5 e^{- 2 x} d x$
3634	Evaluate the Integral	integral from 4 to 9 of 1/( square root of x) with respect to x	$\int_{4}^{9} \frac{1}{\sqrt{x}} d x$
3635	Evaluate the Integral	integral of 4x^3sin(x^4) with respect to x	$\int 4 x^{3} \sin (x^{4}) d x$
3636	Evaluate the Integral	integral of 4 cube root of x^2 with respect to x	$\int 4 \sqrt[3]{x^{2}} d x$
3637	Find the Tangent Line at the Point	square root of x , (1,1)	$\int \frac{e^{2 t}}{1 + 6 e^{2 t} + 9 e^{4 t}} d t$
3638	Find dy/dx	y^3=x^5	$y^{3} = x^{5}$
3639	Evaluate the Integral	integral of (2x)/( square root of x^2+2x+26) with respect to x	$\int \frac{2 x}{\sqrt{x^{2} + 2 x + 26}} d x$
3640	Evaluate the Integral	integral of cot(x) natural log of sin(x) with respect to x	$\int \cot (x) \ln (\sin (x)) d x$
3641	Evaluate the Integral	integral of csc(5x) with respect to x	$\int \csc (5 x) d x$
3642	Evaluate the Integral	integral of arctan(2x) with respect to x	$\int \arctan (2 x) d x$
3643	Evaluate the Integral	integral of arctan(4x) with respect to x	$\int \arctan (4 x) d x$
3644	Evaluate the Integral	integral of cos( square root of t) with respect to t	$\int \cos (\sqrt{t}) d t$
3645	Evaluate the Integral	integral of sin(x)e^(cos(x)) with respect to x	$\int \sin (x) e^{\cos (x)} d x$
3646	Evaluate the Integral	integral of sin(x)cos(2x) with respect to x	$\int \sin (x) \cos (2 x) d x$
3647	Evaluate the Integral	integral of xsin(6x) with respect to x	$\int x \sin (6 x) d x$
3648	Evaluate the Integral	integral of xsin(2x^2) with respect to x	$\int x \sin (2 x^{2}) d x$
3649	Evaluate the Integral	integral of xsin(x/2) with respect to x	$\int x \sin (\frac{x}{2}) d x$
3650	Evaluate the Integral	integral of tsin(2t) with respect to t	$\int t \sin (2 t) d t$
3651	Evaluate the Integral	integral of x(x-4)^9 with respect to x	$\int x {(x - 4)}^{9} d x$
3652	Evaluate the Integral	integral of x(x+1)^8 with respect to x	$\int x {(x + 1)}^{8} d x$
3653	Evaluate the Integral	integral of x(8x+7)^8 with respect to x	$\int x {(8 x + 7)}^{8} d x$
3654	Evaluate the Integral	integral from 0 to pi/4 of 7sec(x)tan(x) with respect to x	$\int_{0}^{\frac{π}{4}} 7 \sec (x) \tan (x) d x$
3655	Evaluate the Integral	integral from 0 to pi/4 of 9sec(x)tan(x) with respect to x	$\int_{0}^{\frac{π}{4}} 9 \sec (x) \tan (x) d x$
3656	Evaluate the Integral	integral from 0 to pi/4 of sin(x) with respect to x	$\int_{0}^{\frac{π}{4}} \sin (x) d x$
3657	Evaluate the Integral	integral from 0 to square root of 3 of (6x)/( square root of x^2+1) with respect to x	$\int_{0}^{\sqrt{3}} \frac{6 x}{\sqrt{x^{2} + 1}} d x$
3658	Evaluate the Integral	integral from 0 to square root of pi of xsin(x^2) with respect to x	$\int_{0}^{\sqrt{π}} x \sin (x^{2}) d x$
3659	Evaluate the Integral	integral from 0 to 1 of 1/( square root of 1-x^2) with respect to x	$\int_{0}^{1} \frac{1}{\sqrt{1 - x^{2}}} d x$
3660	Evaluate the Integral	integral from 0 to 1 of (2t-1)^2 with respect to t	$\int_{0}^{1} {(2 t - 1)}^{2} d t$
3661	Evaluate the Integral	integral from 0 to 2 of (1-4x)^2 with respect to x	$\int_{0}^{2} {(1 - 4 x)}^{2} d x$
3662	Evaluate the Integral	integral from 0 to 8 of 2p*((0.5x) square root of 1+(0.5)^2) with respect to x	$\int_{0}^{8} 2 p \cdot ((0.5 x) \sqrt{1 + {(0.5)}^{2}}) d x$
3663	Evaluate the Integral	integral from 0 to 9 of f(x) with respect to x	$\int_{0}^{9} f (x) d x$
3664	Evaluate the Integral	integral from 0 to natural log of 2 of e^(2x) with respect to x	$\int_{0}^{\ln (2)} e^{2 x} d x$
3665	Evaluate the Integral	integral from 0 to natural log of 2 of xe^x with respect to x	$\int_{0}^{\ln (2)} x e^{x} d x$
3666	Evaluate the Integral	integral from 0 to b of 9x^8 with respect to x	$\int_{0}^{b} 9 x^{8} d x$
3667	Evaluate the Integral	integral from 0 to 4 of f(x) with respect to x	$\int_{0}^{4} f (x) d x$
3668	Evaluate the Integral	integral from 0 to 5 of 4x with respect to x	$\int_{0}^{5} 4 x d x$
3669	Evaluate the Integral	integral from 0 to 5 of \|2x-5\| with respect to x	$\int_{0}^{5} \| 2 x - 5 \| d x$
3670	Evaluate the Integral	integral from 0 to 2pi of xsin(x) with respect to x	$\int_{0}^{2 π} x \sin (x) d x$
3671	Evaluate the Integral	integral from 0 to 2 of 8xe^(x^2) with respect to x	$\int_{0}^{2} 8 x e^{x^{2}} d x$
3672	Evaluate the Integral	integral from 0 to pi of xcos(x) with respect to x	$\int_{0}^{π} x \cos (x) d x$
3673	Evaluate the Integral	integral from -1 to -1 of 4x-4 with respect to x	$\int_{- 1}^{- 1} 4 x - 4 d x$
3674	Evaluate the Integral	integral from -1 to 1 of x^100 with respect to x	$\int_{- 1}^{1} x^{100} d x$
3675	Evaluate the Integral	integral from 1 to 16 of (x-3)/( square root of x) with respect to x	$\int_{1}^{16} \frac{x - 3}{\sqrt{x}} d x$
3676	Evaluate the Integral	integral from 1 to 2 of 3x^5-2x^3 with respect to x	$\int_{1}^{2} 3 x^{5} - 2 x^{3} d x$
3677	Evaluate the Integral	integral from 1 to 3 of 3t^2+7 with respect to t	$\int_{1}^{3} 3 t^{2} + 7 d t$
3678	Evaluate the Integral	integral from 2 to 5 of 4-2x with respect to x	$\int_{2}^{5} 4 - 2 x d x$
3679	Evaluate the Integral	integral from -2 to -1 of 2x(4-x^2)^3 with respect to x	$\int_{- 2}^{- 1} 2 x {(4 - x^{2})}^{3} d x$
3680	Evaluate the Integral	integral from -2 to -1 of u-1/(u^2) with respect to u	$\int_{- 2}^{- 1} u - \frac{1}{u^{2}} d u$
3681	Evaluate the Integral	integral of 1-cos(x) with respect to x	$\int 1 - \cos (x) d x$
3682	Evaluate the Integral	integral of 144-x^2 with respect to x	$\int 144 - x^{2} d x$
3683	Evaluate the Integral	integral of 14x with respect to x	$\int 14 x d x$
3684	Evaluate the Integral	integral of 16x natural log of 2x with respect to x	$\int 16 x \ln (2 x) d x$
3685	Evaluate the Integral	integral of 16 with respect to x	$\int 16 d x$
3686	Evaluate the Integral	integral from 1 to e of 1/x with respect to x	$\int_{1}^{e} \frac{1}{x} d x$
3687	Evaluate the Integral	integral from 1 to e of x^2 natural log of x with respect to x	$\int_{1}^{e} x^{2} \ln (x) d x$
3688	Evaluate the Integral	integral from 1 to 9 of 9x^2 with respect to x	$\int_{1}^{9} 9 x^{2} d x$
3689	Evaluate the Integral	integral of 11(11x-7)^2 with respect to x	$\int 11 {(11 x - 7)}^{2} d x$
3690	Evaluate the Integral	integral of 10x-3 with respect to x	$\int 10 x - 3 d x$
3691	Evaluate the Integral	integral of -10x^4 with respect to x	$\int - 10 x^{4} d x$
3692	Evaluate	12/((2-3(1/3))^3)	$\frac{12}{{(2 - 3 (\frac{1}{3}))}^{3}}$
3693	Evaluate	24/4+12	$\frac{24}{4} + 12$
3694	Evaluate	-(3(3)^2(-7))/(2(3)^3-(-7))	$- \frac{3 {(3)}^{2} (- 7)}{2 {(3)}^{3} - (- 7)}$
3695	Find the Derivative - d/d@VAR	f(x)=x^2+8	$f (x) = x^{2} + 8$
3696	Find the Derivative - d/d@VAR	f(x)=x/(x+1)	$f (x) = \frac{x}{x + 1}$
3697	Evaluate the Integral	integral of sin(3x)cos(5x) with respect to x	$\int \sin (3 x) \cos (5 x) d x$
3698	Find the Derivative - d/d@VAR	f(x)=8x^3	$f (x) = 8 x^{3}$
3699	Evaluate the Limit	limit as x approaches 2 of (x-2)/(x^3-8)	$lim_{x \to 2} \frac{x - 2}{x^{3} - 8}$
3700	Simplify	( square root of x-1)^2	${(\sqrt{x - 1})}^{2}$