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Popular Calculus Problems

integral from-1 to 3 of e^{x+1}	\int\:_{-1}^{3}e^{x+1}dx
integral from 0 to 1 of xsqrt(24x^2+25)	\int\:_{0}^{1}x\sqrt{24x^{2}+25}dx
integral from 0 to 1 of (x^3)/3	\int\:_{0}^{1}\frac{x^{3}}{3}dx
integral from 1 to 7 of 3/x	\int\:_{1}^{7}\frac{3}{x}dx
integral from 2 to 3 of (x^3-1/x)	\int\:_{2}^{3}(x^{3}-\frac{1}{x})dx
integral from pi to ln(x) of cos(e^t)	\int\:_{π}^{\ln(x)}\cos(e^{t})dt
integral from 1 to 2 of (2x)/((x^2+3)^3)	\int\:_{1}^{2}\frac{2x}{(x^{2}+3)^{3}}dx
integral from-2 to 2 of x^2(x+2)	\int\:_{-2}^{2}x^{2}(x+2)dx
integral from 1 to 6 of 1/(sqrt(x^2+2x))	\int\:_{1}^{6}\frac{1}{\sqrt{x^{2}+2x}}dx
integral from 1 to infinity of 1/(x-1)	\int\:_{1}^{\infty\:}\frac{1}{x-1}dx
integral from 0 to 1 of 1/(sqrt(4-x))	\int\:_{0}^{1}\frac{1}{\sqrt{4-x}}dx
integral from 6 to 11 of 4x-10xe^{-0.2x}	\int\:_{6}^{11}4x-10xe^{-0.2x}dx
integral from 1 to 3 of 5x+4	\int\:_{1}^{3}5x+4dx
integral from-infinity to 0 of 1/(x^2+4)	\int\:_{-\infty\:}^{0}\frac{1}{x^{2}+4}dx
integral from 0 to 2 of x^2cos((npix)/2)	\int\:_{0}^{2}x^{2}\cos(\frac{nπx}{2})dx
integral from 0 to e+1 of (x+1)/(x^2-1)	\int\:_{0}^{e+1}\frac{x+1}{x^{2}-1}dx
integral from 1 to 2 of (2x+5)	\int\:_{1}^{2}(2x+5)dx
integral from 0 to pi of sin(x+nx)	\int\:_{0}^{π}\sin(x+nx)dx
integral from 0 to 2 of sqrt(x+2)-x	\int\:_{0}^{2}\sqrt{x+2}-xdx
integral from 2 to 4 of (x-2)/(x^2-5x+4)	\int\:_{2}^{4}\frac{x-2}{x^{2}-5x+4}dx
integral from-1 to 1 of 1/(sqrt(1+x^2))	\int\:_{-1}^{1}\frac{1}{\sqrt{1+x^{2}}}dx
integral from 2 to 5 of 1/(x^2+x-2)	\int\:_{2}^{5}\frac{1}{x^{2}+x-2}dx
integral from 0 to 1 of (4-x^2)	\int\:_{0}^{1}(4-x^{2})dx
integral from 3 to 4 of (x^2-2x-3)	\int\:_{3}^{4}(x^{2}-2x-3)dx
integral from 1 to infinity of e^{-st}t	\int\:_{1}^{\infty\:}e^{-st}tdt
integral from 0 to 2pi of (1+cos(θ))^2	\int\:_{0}^{2π}(1+\cos(θ))^{2}dθ
integral from 0 to 2 of 5-x^2	\int\:_{0}^{2}5-x^{2}dx
integral from 0 to 2pi of (cos(θ))	\int\:_{0}^{2π}(\cos(θ))dθ
integral from-x to x of sin(t)	\int\:_{-x}^{x}\sin(t)dt
integral from 2 to infinity of 9x^{-2}	\int\:_{2}^{\infty\:}9x^{-2}dx
integral from 0 to t of (1-e^u)/u	\int\:_{0}^{t}\frac{1-e^{u}}{u}du
integral from 0 to 2pi of cos(x)*sin(x)	\int\:_{0}^{2π}\cos(x)\cdot\:\sin(x)dx
integral from 1 to 3 of cos(x)+e^x-2x	\int\:_{1}^{3}\cos(x)+e^{x}-2xdx
integral from 100 to 120 of 600x^{-2}	\int\:_{100}^{120}600x^{-2}dx
integral from-pi/2 to pi/2 of 2cos^2(x)	\int\:_{-\frac{π}{2}}^{\frac{π}{2}}2\cos^{2}(x)dx
integral from 2 to 4 of x/((x^2+4)^3)	\int\:_{2}^{4}\frac{x}{(x^{2}+4)^{3}}dx
integral from-1 to 3 of 1/((t+2)^2)	\int\:_{-1}^{3}\frac{1}{(t+2)^{2}}dt
integral from 0 to 9 of 3sqrt(x)	\int\:_{0}^{9}3\sqrt{x}dx
integral from 0 to 1/2 of 1/(1+x^3)	\int\:_{0}^{\frac{1}{2}}\frac{1}{1+x^{3}}dx
integral from 0 to 1 of 3r^2e^{r^3}	\int\:_{0}^{1}3r^{2}e^{r^{3}}dr
integral from 2 to 5 of 2x^2	\int\:_{2}^{5}2x^{2}dx
integral from-1 to 1 of x/(5-4x)	\int\:_{-1}^{1}\frac{x}{5-4x}dx
integral from 1 to 3 of (x-1)/(sqrt(x))	\int\:_{1}^{3}\frac{x-1}{\sqrt{x}}dx
integral from 1 to infinity of 2/(3x+9)	\int\:_{1}^{\infty\:}\frac{2}{3x+9}dx
integral from-1 to 1 of 3/2 x^3	\int\:_{-1}^{1}\frac{3}{2}x^{3}dx
integral from x to 6x of cos(t^2)	\int\:_{x}^{6x}\cos(t^{2})dt
integral from 0 to cot(x) of 1/(1+x^2)	\int\:_{0}^{\cot(x)}\frac{1}{1+x^{2}}dx
integral from 1 to 2 of (x^2-3x+2)	\int\:_{1}^{2}(x^{2}-3x+2)dx
integral from 1 to 9 of (4(ln(x))^3)/x	\int\:_{1}^{9}\frac{4(\ln(x))^{3}}{x}dx
integral from 1 to 2 of x^{-1}+x^4	\int\:_{1}^{2}x^{-1}+x^{4}dx
integral from 0 to pi/2 of x^3cos(x^2)	\int\:_{0}^{\frac{π}{2}}x^{3}\cos(x^{2})dx
integral from 5 to 6 of 3t^2-24t+45	\int\:_{5}^{6}3t^{2}-24t+45dt
integral from-3 to 1 of (x^3+x-5)	\int\:_{-3}^{1}(x^{3}+x-5)dx
integral from-1 to 2 of 1/(x^2+2x+10)	\int\:_{-1}^{2}\frac{1}{x^{2}+2x+10}dx
integral from 1 to x of 1/(1+t^4)	\int\:_{1}^{x}\frac{1}{1+t^{4}}dt
integral from 0 to 4 of (x+sqrt(x))	\int\:_{0}^{4}(x+\sqrt{x})dx
integral from 0 to pi of-x^2+pix-sin(x)	\int\:_{0}^{π}-x^{2}+πx-\sin(x)dx
integral from pi/2 to pi of sin(nx)	\int\:_{\frac{π}{2}}^{π}\sin(nx)dx
integral from 0 to 8 of xe^{x^2}	\int\:_{0}^{8}xe^{x^{2}}dx
integral from 0 to 8 of sqrt(64-t^2)	\int\:_{0}^{8}\sqrt{64-t^{2}}dt
integral from 0 to 1 of x^3-sqrt(x)	\int\:_{0}^{1}x^{3}-\sqrt{x}dx
integral from 1 to-1 of (r+1)^2	\int\:_{1}^{-1}(r+1)^{2}dr
integral from pi/4 to pi/2 of 2-csc^2(x)	\int\:_{\frac{π}{4}}^{\frac{π}{2}}2-\csc^{2}(x)dx
integral from 1 to 3 of x^3-4x^2+3x	\int\:_{1}^{3}x^{3}-4x^{2}+3xdx
integral from x to 4x of 2^{sqrt(t)}	\int\:_{x}^{4x}2^{\sqrt{t}}dt
integral from 2 to 8 of (2-x)(x-8)	\int\:_{2}^{8}(2-x)(x-8)dx
integral from \sqrt[3]{x} to 3pi of cos(t^3)	\int\:_{\sqrt[3]{x}}^{3π}\cos(t^{3})dt
integral from pi/2 to pi of (-xcos(x))	\int\:_{\frac{π}{2}}^{π}(-x\cos(x))dx
integral from 0 to 10 of 2x	\int\:_{0}^{10}2xdx
integral from-1 to 1 of (x^3-2x^2+4x)	\int\:_{-1}^{1}(x^{3}-2x^{2}+4x)dx
integral from-pi to pi of 7sin(x)	\int\:_{-π}^{π}7\sin(x)dx
integral from 0 to 1/3 of 1/(36x^2+4)	\int\:_{0}^{\frac{1}{3}}\frac{1}{36x^{2}+4}dx
integral from 0 to 1 of xθx^{θ-1}	\int\:_{0}^{1}xθx^{θ-1}dx
integral from-1 to 1 of 2e^{-3t+8}	\int\:_{-1}^{1}2e^{-3t+8}dt
integral from 0 to 1 of e^{-5x}	\int\:_{0}^{1}e^{-5x}dx
integral from 0 to 1 of x^7e^{x^4}	\int\:_{0}^{1}x^{7}e^{x^{4}}dx
integral from 1 to 2 of [ 1/x-2/(x^3)]	\int\:_{1}^{2}[\frac{1}{x}-\frac{2}{x^{3}}]dx
integral from 0 to pi/2 of 0	\int\:_{0}^{\frac{π}{2}}0dx
integral from 1 to 3 of-x/3+1	\int\:_{1}^{3}-\frac{x}{3}+1dx
integral from 0 to 1 of x-x^5	\int\:_{0}^{1}x-x^{5}dx
integral from-1 to 1 of t^5	\int\:_{-1}^{1}t^{5}dt
integral from 0 to 2 of (8-2x^2)	\int\:_{0}^{2}(8-2x^{2})dx
integral from x to x^2 of t^3	\int\:_{x}^{x^{2}}t^{3}dt
integral from 0 to 3 of-x+3	\int\:_{0}^{3}-x+3dx
integral from 1 to 6 of \|3x-9\|	\int\:_{1}^{6}\left\|3x-9\right\|dx
integral from 1 to 2 of sqrt(1+x)	\int\:_{1}^{2}\sqrt{1+x}dx
integral from 0 to 1 of (y+1)sqrt(1-y)	\int\:_{0}^{1}(y+1)\sqrt{1-y}dy
integral from 0 to 1 of (3x+5)^6	\int\:_{0}^{1}(3x+5)^{6}dx
integral from 1 to 2 of x(ln(x))^2	\int\:_{1}^{2}x(\ln(x))^{2}dx
integral from 0 to pi/4 of e^{-2it}	\int\:_{0}^{\frac{π}{4}}e^{-2it}dt
integral from 1 to 3 of (2(ln(x))^2)/x	\int\:_{1}^{3}\frac{2(\ln(x))^{2}}{x}dx
integral from-1 to 1 of \|x\|e^{(1+x^2)}	\int\:_{-1}^{1}\left\|x\right\|e^{(1+x^{2})}dx
integral from 0 to 1/e of 1/(xln^2(x))	\int\:_{0}^{\frac{1}{e}}\frac{1}{x\ln^{2}(x)}dx
integral from-1 to 2 of (x^2+x+1)	\int\:_{-1}^{2}(x^{2}+x+1)dx
integral from-2021 to 2021 of x^3	\int\:_{-2021}^{2021}x^{3}dx
integral from-2 to 2 of-x^2-4	\int\:_{-2}^{2}-x^{2}-4dx
integral from 1 to 3 of (x^2-2x)	\int\:_{1}^{3}(x^{2}-2x)dx
integral from-5 to 0 of 2-sqrt(25-x^2)	\int\:_{-5}^{0}2-\sqrt{25-x^{2}}dx
integral from-2 to 1 of 1/((11+5x)^2)	\int\:_{-2}^{1}\frac{1}{(11+5x)^{2}}dx
integral from 1 to e^{-x^2 of}[ln(t)]^4	\int\:_{1}^{e^{-x^{2}}}[\ln(t)]^{4}dt

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