Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
8601	Evaluate the Integral	integral of (2x+2)/((x^2+2x-4)^4) with respect to x	$\int \frac{2 x + 2}{{(x^{2} + 2 x - 4)}^{4}} d x$
8602	Evaluate the Integral	integral of (2x+7)/((2x^2+14x)^4) with respect to x	$\int \frac{2 x + 7}{{(2 x^{2} + 14 x)}^{4}} d x$
8603	Evaluate the Integral	integral of (2x-4)/(3x^2-12x+1) with respect to x	$\int \frac{2 x - 4}{3 x^{2} - 12 x + 1} d x$
8604	Evaluate the Integral	integral of (3e^x)/(4+e^x) with respect to x	$\int \frac{3 e^{x}}{4 + e^{x}} d x$
8605	Evaluate the Integral	integral of r^2e^(-(2r)/a) with respect to r	$\int r^{2} e^{- \frac{2 r}{a}} d r$
8606	Evaluate the Integral	integral of sec(x)^4 with respect to x	$\int \sec^{4} (x) d x$
8607	Evaluate the Integral	integral of re^(r/2) with respect to r	$\int r e^{\frac{r}{2}} d r$
8608	Evaluate the Integral	integral of re^(-r^2) with respect to r	$\int r e^{- r^{2}} d r$
8609	Evaluate the Integral	integral from pi/4 to pi/3 of sec(x)tan(x) with respect to x	$\int_{\frac{π}{4}}^{\frac{π}{3}} \sec (x) \tan (x) d x$
8610	Evaluate the Integral	integral from pi/4 to cot(x) of csc(y)^2 with respect to y	$\int_{\frac{π}{4}}^{\cot (x)} \csc^{2} (y) d y$
8611	Evaluate the Integral	integral from -pi/6 to pi/6 of sec(x)^2 with respect to x	$\int_{- \frac{π}{6}}^{\frac{π}{6}} \sec^{2} (x) d x$
8612	Evaluate the Integral	integral from pi/8 to pi/4 of 8csc(2x)-8cot(2x) with respect to x	$\int_{\frac{π}{8}}^{\frac{π}{4}} 8 \csc (2 x) - 8 \cot (2 x) d x$
8613	Evaluate the Integral	integral from pi/6 to pi/2 of cot(x) with respect to x	$\int_{\frac{π}{6}}^{\frac{π}{2}} \cot (x) d x$
8614	Evaluate the Integral	integral from -pi/6 to pi/6 of 5sec(x)^2 with respect to x	$\int_{- \frac{π}{6}}^{\frac{π}{6}} 5 \sec^{2} (x) d x$
8615	Evaluate the Integral	integral of sin(pix)^2cos(pix)^5 with respect to x	$\int \sin^{2} (π x) \cos^{5} (π x) d x$
8616	Evaluate the Integral	integral of sin(t)^2 with respect to t	$\int \sin^{2} (t) d t$
8617	Evaluate the Integral	integral of sin(3x)^2cos(3x) with respect to x	$\int \sin^{2} (3 x) \cos (3 x) d x$
8618	Evaluate the Integral	integral of sin(x)^5cos(x) with respect to x	$\int \sin^{5} (x) \cos (x) d x$
8619	Evaluate the Integral	integral of (sin(y))/y with respect to y	$\int \frac{\sin (y)}{y} d y$
8620	Evaluate the Integral	integral of (sin(x))/( square root of cos(x)^3) with respect to x	$\int \frac{\sin (x)}{\sqrt{\cos^{3} (x)}} d x$
8621	Evaluate the Integral	integral of (sin(x))/(1-cos(x)) with respect to x	$\int \frac{\sin (x)}{1 - \cos (x)} d x$
8622	Evaluate the Integral	integral of sin(x)^2cos(x)^4 with respect to x	$\int \sin^{2} (x) \cos^{4} (x) d x$
8623	Find the Linearization at a=π/3	f(x)=sin(x) , a=pi/3	$\int \frac{\sin (4 x)}{\cos (2 x)} d x$
8624	Evaluate the Integral	integral of sec(x)^4tan(x)^4 with respect to x	$\int \sec^{4} (x) \tan^{4} (x) d x$
8625	Evaluate the Integral	integral of sec(4x+1)^2 with respect to x	$\int \sec^{2} (4 x + 1) d x$
8626	Evaluate the Integral	integral of sec(5x)^2 with respect to x	$\int \sec^{2} (5 x) d x$
8627	Evaluate the Integral	integral of square root of e^x with respect to x	$\int \sqrt{e^{x}} d x$
8628	Evaluate the Integral	integral of te^(-t^2) with respect to t	$\int t e^{- t^{2}} d t$
8629	Evaluate the Integral	integral of tan(x)^9sec(x)^2 with respect to x	$\int \tan^{9} (x) \sec^{2} (x) d x$
8630	Evaluate the Integral	integral of u^3 with respect to u	$\int u^{3} d u$
8631	Evaluate the Integral	integral of u^2 with respect to u	$\int u^{2} d u$
8632	Evaluate the Integral	integral of te^(-t) with respect to t	$\int t e^{- t} d t$
8633	Evaluate the Integral	integral of square root of 1+4x^3(12x^2) with respect to x	$\int \sqrt{1 + 4 x^{3}} (12 x^{2}) d x$
8634	Evaluate the Integral	integral of square root of 16-9x^2 with respect to x	$\int \sqrt{16 - 9 x^{2}} d x$
8635	Evaluate the Integral	integral of square root of x^2-4 with respect to x	$\int \sqrt{x^{2} - 4} d x$
8636	Evaluate the Integral	integral of (3x+5)^2 with respect to x	$\int {(3 x + 5)}^{2} d x$
8637	Evaluate the Integral	integral of sin(x)^n with respect to x	$\int {\sin (x)}^{n} d x$
8638	Evaluate the Integral	integral of sin(x)^7cos(x)^5 with respect to x	$\int \sin^{7} (x) \cos^{5} (x) d x$
8639	Evaluate the Integral	integral of t^(-1/2) with respect to t	$\int t^{- \frac{1}{2}} d t$
8640	Evaluate the Integral	integral of sin(3x)^5cos(3x) with respect to x	$\int \sin^{5} (3 x) \cos (3 x) d x$
8641	Evaluate the Integral	integral of sin(2x)^3 square root of cos(2x) with respect to x	$\int \sin^{3} (2 x) \sqrt{\cos (2 x)} d x$
8642	Evaluate the Integral	integral of sin(y)^2 with respect to y	$\int \sin^{2} (y) d y$
8643	Evaluate the Integral	integral of (tan(x))/(cos(x)) with respect to x	$\int \frac{\tan (x)}{\cos (x)} d x$
8644	Evaluate the Integral	integral of tan(3x)^3 with respect to x	$\int \tan^{3} (3 x) d x$
8645	Evaluate the Integral	integral of tan(4x)^3 with respect to x	$\int \tan^{3} (4 x) d x$
8646	Evaluate the Integral	integral of tan(x)^3sec(x)^4 with respect to x	$\int \tan^{3} (x) \sec^{4} (x) d x$
8647	Evaluate the Integral	integral of tan(2x)^4sec(2x)^4 with respect to x	$\int \tan^{4} (2 x) \sec^{4} (2 x) d x$
8648	Evaluate the Integral	integral of t^2cos(t) with respect to t	$\int t^{2} \cos (t) d t$
8649	Evaluate the Integral	integral of t^3 square root of 2t^4+3 with respect to t	$\int t^{3} \sqrt{2 t^{4} + 3} d t$
8650	Evaluate the Integral	integral of (tan(x))/(cos(x)^2) with respect to x	$\int \frac{\tan (x)}{\cos^{2} (x)} d x$
8651	Evaluate the Integral	integral of 1/(5-3x) with respect to xdx	$\int \frac{1}{5 - 3 x} d x d x$
8652	Evaluate the Integral	integral of 1/(x^6) with respect to xdx	$\int \frac{1}{x^{6}} d x d x$
8653	Evaluate the Integral	integral of 1/(x^9) with respect to xdx	$\int \frac{1}{x^{9}} d x d x$
8654	Evaluate the Integral	integral of 1/(x^2 square root of 9-x^2) with respect to xdx	$\int \frac{1}{x^{2} \sqrt{9 - x^{2}}} d x d x$
8655	Evaluate the Integral	integral of 1/((1-6t)^4) with respect to tdt	$\int \frac{1}{{(1 - 6 t)}^{4}} d t d t$
8656	Evaluate the Integral	integral of csc(x)^4 with respect to x	$\int \csc^{4} (x) d x$
8657	Evaluate the Integral	integral of csc(4x)^2 with respect to x	$\int \csc^{2} (4 x) d x$
8658	Evaluate the Integral	integral of csc(2x)^2 with respect to x	$\int \csc^{2} (2 x) d x$
8659	Evaluate the Integral	integral of csc(3)^2 with respect to x	$\int \csc^{2} (3) d x$
8660	Evaluate the Summation	sum from n=2 to 10 of -2n-3	$\sum_{n = 2}^{10} - 2 n - 3$
8661	Evaluate the Integral	integral of cot(x)^4 with respect to x	$\int \cot^{4} (x) d x$
8662	Evaluate the Integral	integral of cot(7x)^2 with respect to x	$\int \cot^{2} (7 x) d x$
8663	Evaluate the Integral	integral of (cot(x))/(sin(x)^2) with respect to x	$\int \frac{\cot (x)}{\sin^{2} (x)} d x$
8664	Evaluate the Integral	integral of cos(x)^7 with respect to x	$\int \cos^{7} (x) d x$
8665	Evaluate the Integral	integral of cos(x)^7sin(x) with respect to x	$\int \cos^{7} (x) \sin (x) d x$
8666	Evaluate the Integral	integral of cos(2x)^4sin(2x) with respect to x	$\int \cos^{4} (2 x) \sin (2 x) d x$
8667	Evaluate the Integral	integral of cos(x)^3 square root of sin(x) with respect to x	$\int \cos^{3} (x) \sqrt{\sin (x)} d x$
8668	Evaluate the Integral	integral of cos(6x)^3 with respect to x	$\int \cos^{3} (6 x) d x$
8669	Evaluate the Integral	integral of cos(20x)^3 with respect to x	$\int \cos^{3} (20 x) d x$
8670	Evaluate the Integral	integral of e^(-0.02x) with respect to x	$\int e^{- 0.02 x} d x$
8671	Evaluate the Integral	integral of e^(0.04x) with respect to x	$\int e^{0.04 x} d x$
8672	Evaluate the Integral	integral of e^(x^2)x with respect to x	$\int e^{x^{2}} x d x$
8673	Evaluate the Integral	integral of 1/y with respect to ydy	$\int \frac{1}{y} d y d y$
8674	Evaluate the Integral	integral of 1/(dx) with respect to ydx	$\int \frac{1}{d x} d y d x$
8675	Evaluate the Integral	integral of e^(-0.125x) with respect to x	$\int e^{- 0.125 x} d x$
8676	Evaluate the Integral	integral of e^(1/2x) with respect to x	$\int e^{\frac{1}{2} x} d x$
8677	Evaluate the Integral	integral of e^(-2x)sin(2x) with respect to x	$\int e^{- 2 x} \sin (2 x) d x$
8678	Evaluate the Integral	integral of e^(-0.1x) with respect to x	$\int e^{- 0.1 x} d x$
8679	Evaluate the Integral	integral of e^(13x) with respect to x	$\int e^{13 x} d x$
8680	Evaluate the Integral	integral of e^xtan(e^x) with respect to x	$\int e^{x} \tan (e^{x}) d x$
8681	Evaluate the Integral	integral of e^(-x)sin(4x) with respect to x	$\int e^{- x} \sin (4 x) d x$
8682	Evaluate the Integral	integral of e^xsin(e^x) with respect to x	$\int e^{x} \sin (e^{x}) d x$
8683	Evaluate the Integral	integral of ( natural log of 7x)/x with respect to x	$\int \frac{\ln (7 x)}{x} d x$
8684	Evaluate the Integral	integral of ( natural log of x)/(x square root of 1+ natural log of x) with respect to x	$\int \frac{\ln (x)}{x \sqrt{1 + \ln (x)}} d x$
8685	Evaluate the Integral	integral from -pi/2 to pi/2 of sin(x) with respect to x	$\int_{- \frac{π}{2}}^{\frac{π}{2}} \sin (x) d x$
8686	Evaluate the Integral	integral of ( natural log of z)/z with respect to z	$\int \frac{\ln (z)}{z} d z$
8687	Evaluate the Integral	integral from pi/3 to 2pi of 4cos(x)^3sin(x) with respect to x	$\int_{\frac{π}{3}}^{2 π} 4 \cos^{3} (x) \sin (x) d x$
8688	Evaluate the Integral	integral from pi/2 to pi of sin(x) with respect to x	$\int_{\frac{π}{2}}^{π} \sin (x) d x$
8689	Evaluate the Integral	integral from pi/2 to pi of 2cot(x/3) with respect to x	$\int_{\frac{π}{2}}^{π} 2 \cot (\frac{x}{3}) d x$
8690	Evaluate the Integral	integral of e^(sin(pix))cos(pix) with respect to x	$\int e^{\sin (π x)} \cos (π x) d x$
8691	Evaluate the Integral	integral of e^x*(2x) with respect to x	$\int e^{x} \cdot (2 x) d x$
8692	Evaluate the Integral	integral of e^x square root of 1-e^(2x) with respect to x	$\int e^{x} \sqrt{1 - e^{2 x}} d x$
8693	Evaluate the Integral	integral of e^(6x)cos(5x) with respect to x	$\int e^{6 x} \cos (5 x) d x$
8694	Evaluate the Integral	integral of e^(8x)sin(9x) with respect to x	$\int e^{8 x} \sin (9 x) d x$
8695	Evaluate the Integral	integral of e^(3x)+5e^(-x) with respect to x	$\int e^{3 x} + 5 e^{- x} d x$
8696	Evaluate the Integral	integral of e^(4t) with respect to t	$\int e^{4 t} d t$
8697	Evaluate the Integral	integral of e^(4x)cos(3x) with respect to x	$\int e^{4 x} \cos (3 x) d x$
8698	Evaluate the Integral	integral of x^1.5 with respect to x	$\int x^{1.5} d x$
8699	Evaluate the Integral	integral of x^-0.3 with respect to x	$\int x^{- 0.3} d x$
8700	Evaluate the Integral	integral of x^(7/6) with respect to x	$\int x^{\frac{7}{6}} d x$