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Popular Calculus Problems

integral from 0 to 3pi of xsin(x)	\int\:_{0}^{3π}x\sin(x)dx
integral from 1 to 4 of xe^x	\int\:_{1}^{4}xe^{x}dx
integral from 0 to 9 of (81-x^2)	\int\:_{0}^{9}(81-x^{2})dx
integral from-1 to 0 of (x+4)cos(npix)	\int\:_{-1}^{0}(x+4)\cos(nπx)dx
integral from 0 to 2 of x^2sqrt(x^3+5)	\int\:_{0}^{2}x^{2}\sqrt{x^{3}+5}dx
integral from 0 to 1 of ln\|1-x\|	\int\:_{0}^{1}\ln\left\|1-x\right\|dx
integral from 4 to 6 of 1/(x-2)	\int\:_{4}^{6}\frac{1}{x-2}dx
integral from 1 to 5 of (3t)/(e^{2t)}	\int\:_{1}^{5}\frac{3t}{e^{2t}}dt
integral from 0 to 4 of e^{(x-2)^4}	\int\:_{0}^{4}e^{(x-2)^{4}}dx
integral from 0 to 2 of (3x-1)^3	\int\:_{0}^{2}(3x-1)^{3}dx
integral from 0 to 1 of (2t)^2	\int\:_{0}^{1}(2t)^{2}dt
integral from 2 to 5 of x(x-3)^4	\int\:_{2}^{5}x(x-3)^{4}dx
integral from a to b of 4x^5(ln(x^3))	\int\:_{a}^{b}4x^{5}(\ln(x^{3}))dx
integral from-5 to-10 of 1	\int\:_{-5}^{-10}1dx
integral from 2 to 4 of x^3-x^5	\int\:_{2}^{4}x^{3}-x^{5}dx
integral from 0 to 2 of ln(x^3)	\int\:_{0}^{2}\ln(x^{3})dx
integral from 3x to 8 of (x+y)/(60)	\int\:_{3x}^{8}\frac{x+y}{60}dy
integral from 1 to k of k/(2w^2)	\int\:_{1}^{k}\frac{k}{2w^{2}}dw
integral from 1 to 5 of x^4ln(x)	\int\:_{1}^{5}x^{4}\ln(x)dx
integral from 7/2 to 8 of 3/(x-2)	\int\:_{\frac{7}{2}}^{8}\frac{3}{x-2}dx
integral from 1 to 2 of \|2x-3\|	\int\:_{1}^{2}\left\|2x-3\right\|dx
integral from 1 to 3 of x^2e^{-x}	\int\:_{1}^{3}x^{2}e^{-x}dx
integral from 0 to 3 of (e^{3/x})/(x^2)	\int\:_{0}^{3}\frac{e^{\frac{3}{x}}}{x^{2}}dx
integral from 0 to 2 of 2/(x^2)	\int\:_{0}^{2}\frac{2}{x^{2}}dx
integral from 0 to 2 of (4x-x^2-x^2)	\int\:_{0}^{2}(4x-x^{2}-x^{2})dx
integral from 4 to infinity of 3/(x^5)	\int\:_{4}^{\infty\:}\frac{3}{x^{5}}dx
integral from 1 to 3 of 2x^2+3	\int\:_{1}^{3}2x^{2}+3dx
integral from 0 to 4 of (x-1)/(x^2+x-2)	\int\:_{0}^{4}\frac{x-1}{x^{2}+x-2}dx
integral from 8 to infinity of 2x^{-3}	\int\:_{8}^{\infty\:}2x^{-3}dx
integral from 1 to 2 of 1/(x+y)	\int\:_{1}^{2}\frac{1}{x+y}dx
integral from 1 to 2 of 1/x+y	\int\:_{1}^{2}\frac{1}{x}+ydx
integral from 8 to 10 of 0.5x^{-1.5}	\int\:_{8}^{10}0.5x^{-1.5}dx
integral from-2 to 2 of (1+2x)	\int\:_{-2}^{2}(1+2x)dx
integral from 1 to 2 of 1/((x-2)^{2/3)}	\int\:_{1}^{2}\frac{1}{(x-2)^{\frac{2}{3}}}dx
integral from 2 to 3 of (3t+2)	\int\:_{2}^{3}(3t+2)dt
integral from 0 to 1 of (3/8)x^2	\int\:_{0}^{1}(\frac{3}{8})x^{2}dx
integral from pi to 0 of-sin^2(x)	\int\:_{π}^{0}-\sin^{2}(x)dx
integral from 6 to 12 of y/(y^2-2y-3)	\int\:_{6}^{12}\frac{y}{y^{2}-2y-3}dy
integral from 0 to 1 of e^x(x+1)	\int\:_{0}^{1}e^{x}(x+1)dx
integral from 1 to 3 of (3x^2)	\int\:_{1}^{3}(3x^{2})dx
integral from 0 to 2 of (x^2+3xy+2y^2)	\int\:_{0}^{2}(x^{2}+3xy+2y^{2})dy
integral from 0 to 1 of (1+2x+x^2)^2	\int\:_{0}^{1}(1+2x+x^{2})^{2}dx
integral from pi to 3pi of sin(x)	\int\:_{π}^{3π}\sin(x)dx
integral from 1 to 2 of 1/((4-x)^3)	\int\:_{1}^{2}\frac{1}{(4-x)^{3}}dx
integral from 1 to 4 of xe^{-2x^2}+6x-2	\int\:_{1}^{4}xe^{-2x^{2}}+6x-2dx
integral from 0 to infinity of kxe^{-2x}	\int\:_{0}^{\infty\:}kxe^{-2x}dx
integral from 0 to 3 of (x)^2	\int\:_{0}^{3}(x)^{2}dx
integral from 2 to infinity of xln(x)	\int\:_{2}^{\infty\:}x\ln(x)dx
integral from 0 to 9-4y^2 of 16y	\int\:_{0}^{9-4y^{2}}16ydy
integral from-3 to 2 of 9-x^2-x-3	\int\:_{-3}^{2}9-x^{2}-x-3dx
integral from 0 to ln(1) of e^{-t^2}	\int\:_{0}^{\ln(1)}e^{-t^{2}}dt
integral from 0 to pi/3 of 4tan(x)	\int\:_{0}^{\frac{π}{3}}4\tan(x)dx
integral from 0 to 6.7 of 2t^3-8.5t	\int\:_{0}^{6.7}2t^{3}-8.5tdt
integral from 1 to 4 of (4sqrt(x)-x)	\int\:_{1}^{4}(4\sqrt{x}-x)dx
integral from 0 to 1 of x((6x)/(x^2+1))	\int\:_{0}^{1}x(\frac{6x}{x^{2}+1})dx
integral from-1 to 1 of 1/(1+e^{-x)}	\int\:_{-1}^{1}\frac{1}{1+e^{-x}}dx
integral from 2 to 3 of x^3arctan(x-1)	\int\:_{2}^{3}x^{3}\arctan(x-1)dx
integral from 2 to 6 of 0.35e^{-0.35x}	\int\:_{2}^{6}0.35e^{-0.35x}dx
integral from 1 to infinity of ne^{-n}	\int\:_{1}^{\infty\:}ne^{-n}dn
integral from-2 to 2 of x^6	\int\:_{-2}^{2}x^{6}dx
integral from 0 to 1 of (12ln(x))	\int\:_{0}^{1}(12\ln(x))dx
integral from-1 to 2 of (x^3-5x^2+3x-1)	\int\:_{-1}^{2}(x^{3}-5x^{2}+3x-1)dx
integral from 1 to 2 of ((x^2+1))/(x^2)	\int\:_{1}^{2}\frac{(x^{2}+1)}{x^{2}}dx
integral from 1 to 7 of (ln(x^2))/(x^3)	\int\:_{1}^{7}\frac{\ln(x^{2})}{x^{3}}dx
integral from 0 to 24 of x^2(1/288 x)	\int\:_{0}^{24}x^{2}(\frac{1}{288}x)dx
integral from 0 to 1 of (36)/(x^2-81)	\int\:_{0}^{1}\frac{36}{x^{2}-81}dx
integral from 0 to pi of 6xsin(x)	\int\:_{0}^{π}6x\sin(x)dx
integral from 0 to 2 of 1/((x-1)^4)	\int\:_{0}^{2}\frac{1}{(x-1)^{4}}dx
integral from 0 to 1 of (-t+1)e^{-st}	\int\:_{0}^{1}(-t+1)e^{-st}dt
integral from 0 to 1/2 of sqrt(9-36x^2)	\int\:_{0}^{\frac{1}{2}}\sqrt{9-36x^{2}}dx
integral from-16 to 16 of 1/(256+x^2)	\int\:_{-16}^{16}\frac{1}{256+x^{2}}dx
integral from 1 to x of xy	\int\:_{1}^{x}xydy
integral from 0 to 1 of (1+x^3)	\int\:_{0}^{1}(1+x^{3})dx
integral from 3 to 0 of (5x+1)	\int\:_{3}^{0}(5x+1)dx
integral from 0 to 6 of t	\int\:_{0}^{6}tdt
integral from-1 to 1 of e^y-(y^2-3)	\int\:_{-1}^{1}e^{y}-(y^{2}-3)dy
integral from 0 to pi of 1/(a+bx)	\int\:_{0}^{π}\frac{1}{a+bx}dx
integral from x to 5x of e^{3t}	\int\:_{x}^{5x}e^{3t}dt
integral from-pi/4 to pi/4 of cos^2(2θ)	\int\:_{-\frac{π}{4}}^{\frac{π}{4}}\cos^{2}(2θ)dθ
integral from 1 to 9 of (1+sqrt(x))	\int\:_{1}^{9}(1+\sqrt{x})dx
integral from 0 to 1 of sin(y)	\int\:_{0}^{1}\sin(y)dy
integral from-6 to 6 of (e^θ+sin(θ))	\int\:_{-6}^{6}(e^{θ}+\sin(θ))dθ
integral from 1 to 3 of (ln(x))/(x^5)	\int\:_{1}^{3}\frac{\ln(x)}{x^{5}}dx
integral from 0 to pi/(12) of 5cos^5(6x)	\int\:_{0}^{\frac{π}{12}}5\cos^{5}(6x)dx
integral from 0 to 7pi of sqrt(x^4+4x^2)	\int\:_{0}^{7π}\sqrt{x^{4}+4x^{2}}dx
integral from 0 to 1 of (3x-1)^3	\int\:_{0}^{1}(3x-1)^{3}dx
integral from 0 to pi/4 of e^xsin(e^x)	\int\:_{0}^{\frac{π}{4}}e^{x}\sin(e^{x})dx
integral from-2 to 3 of (x^2+2)	\int\:_{-2}^{3}(x^{2}+2)dx
integral from 1 to 2 of (x+e^{-y})	\int\:_{1}^{2}(x+e^{-y})dx
integral from 10 to 7 of g(x)	\int\:_{10}^{7}g(x)dx
integral from 1 to 2 of (2x+3/x)^2	\int\:_{1}^{2}(2x+\frac{3}{x})^{2}dx
integral from 0 to 0.9 of e^{-x}	\int\:_{0}^{0.9}e^{-x}dx
integral from 0 to 2x of (2xy^3-x)	\int\:_{0}^{2x}(2xy^{3}-x)dy
integral from-1 to 5 of (4x^3-3x^2+1)	\int\:_{-1}^{5}(4x^{3}-3x^{2}+1)dx
integral from 0 to 2 of xe^{(x^2)/2}	\int\:_{0}^{2}xe^{\frac{x^{2}}{2}}dx
integral from-2 to 2 of 10sqrt(4-x^2)	\int\:_{-2}^{2}10\sqrt{4-x^{2}}dx
integral from-1 to 1 of (3+2x)^2	\int\:_{-1}^{1}(3+2x)^{2}dx
integral from 0 to 2 of (x^3)/3	\int\:_{0}^{2}\frac{x^{3}}{3}dx
integral from 1 to e^3 of 3/x	\int\:_{1}^{e^{3}}\frac{3}{x}dx
integral from-1 to 1 of x^3-2x^2+5	\int\:_{-1}^{1}x^{3}-2x^{2}+5dx

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