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Popular Calculus Problems

integral from pi/4 to pi/2 of cos(3x)	\int\:_{\frac{π}{4}}^{\frac{π}{2}}\cos(3x)dx
integral from 1 to e of (3ln(x))/x	\int\:_{1}^{e}\frac{3\ln(x)}{x}dx
integral from 0 to 1 of 4(1-y)^3	\int\:_{0}^{1}4(1-y)^{3}dy
integral from 0 to infinity of-3e^{-x}	\int\:_{0}^{\infty\:}-3e^{-x}dx
integral from 0 to pi/2 of tsin(t)	\int\:_{0}^{\frac{π}{2}}t\sin(t)dt
integral from-2 to 2 of (1-(x^2)/4)^2	\int\:_{-2}^{2}(1-\frac{x^{2}}{4})^{2}dx
integral from 0 to 2x^2 of 3xy	\int\:_{0}^{2x^{2}}3xydy
integral from-1 to 2 of x(x+1)(x-2)	\int\:_{-1}^{2}x(x+1)(x-2)dx
integral from 0 to 3 of (3-x)^{(-1)/2}	\int\:_{0}^{3}(3-x)^{\frac{-1}{2}}dx
integral from-6 to 1 of \|x^3\|	\int\:_{-6}^{1}\left\|x^{3}\right\|dx
integral from 1 to 2 of (e^{3t}-4/t)	\int\:_{1}^{2}(e^{3t}-\frac{4}{t})dt
integral from 0 to 1 of e^x-e^{7x-6}	\int\:_{0}^{1}e^{x}-e^{7x-6}dx
integral from 3 to 5 of xe^{x^2}	\int\:_{3}^{5}xe^{x^{2}}dx
integral from 1 to 3 of ((3x^2+4x+1)/x)	\int\:_{1}^{3}(\frac{3x^{2}+4x+1}{x})dx
integral from 0 to 1 of tsqrt(9t^2+16)	\int\:_{0}^{1}t\sqrt{9t^{2}+16}dt
integral from-5 to 3 of x^2+2x-15	\int\:_{-5}^{3}x^{2}+2x-15dx
integral from 0 to 2 of (3t-1)^{60}	\int\:_{0}^{2}(3t-1)^{60}dt
integral from 0 to sqrt(4-y^2 of)z(-y+2)	\int\:_{0}^{\sqrt{4-y^{2}}}z(-y+2)dz
integral from 0 to 1 of (5x^2-8x+9)	\int\:_{0}^{1}(5x^{2}-8x+9)dx
integral from 0 to 1 of (x^2-x+1)e^{2x}	\int\:_{0}^{1}(x^{2}-x+1)e^{2x}dx
integral from 0 to 1 of 1/((x^2-1))	\int\:_{0}^{1}\frac{1}{(x^{2}-1)}dx
integral from 5 to 7 of x^2+x+1-15	\int\:_{5}^{7}x^{2}+x+1-15dx
integral from-8 to 8 of \|7x\|-(x^2-8)	\int\:_{-8}^{8}\left\|7x\right\|-(x^{2}-8)dx
integral from 2 to 4 of 5x^4+8x^3	\int\:_{2}^{4}5x^{4}+8x^{3}dx
integral from-1 to 1 of (\sqrt[3]{x}-3)	\int\:_{-1}^{1}(\sqrt[3]{x}-3)dx
integral from 0 to 1 of (2xe^{x^2})	\int\:_{0}^{1}(2xe^{x^{2}})dx
integral from 0 to 16 of 1	\int\:_{0}^{16}1dx
integral from 7 to 9 of 2pix(7/x)	\int\:_{7}^{9}2πx(\frac{7}{x})dx
integral from-2 to 0 of 6x^2-8x	\int\:_{-2}^{0}6x^{2}-8xdx
integral from 0 to 1 of sqrt(5+4t^2)	\int\:_{0}^{1}\sqrt{5+4t^{2}}dt
integral from 0 to 4 of 2e^{-st}	\int\:_{0}^{4}2e^{-st}dt
integral from 0 to 1 of x(2(1-x))	\int\:_{0}^{1}x(2(1-x))dx
integral from 2 to 6 of (2x-3)/2	\int\:_{2}^{6}\frac{2x-3}{2}dx
integral from-3 to 3 of 2x+2	\int\:_{-3}^{3}2x+2dx
integral from-4 to 2 of (-2\|x\|)	\int\:_{-4}^{2}(-2\left\|x\right\|)dx
integral from-3 to 3 of 36-4x^2	\int\:_{-3}^{3}36-4x^{2}dx
integral from 1 to 3 of 1/2 (3^2-1^2)	\int\:_{1}^{3}\frac{1}{2}(3^{2}-1^{2})dx
integral from 0 to 1 of (ln(x+1))/(x^2)	\int\:_{0}^{1}\frac{\ln(x+1)}{x^{2}}dx
integral from 0 to pi/4 of (3cos^2(θ))/2	\int\:_{0}^{\frac{π}{4}}\frac{3\cos^{2}(θ)}{2}dθ
integral from 2 to 6 of 2/x-4/(x^2)	\int\:_{2}^{6}\frac{2}{x}-\frac{4}{x^{2}}dx
integral from 0 to 5 of (10)/(sqrt(x))	\int\:_{0}^{5}\frac{10}{\sqrt{x}}dx
integral from 0 to 6 of (x^2+2)	\int\:_{0}^{6}(x^{2}+2)dx
integral from 0 to pi/2 of (1-cos(2θ))/2	\int\:_{0}^{\frac{π}{2}}\frac{1-\cos(2θ)}{2}dθ
integral from-1 to x of e^t	\int\:_{-1}^{x}e^{t}dt
integral from 0 to 7 of (x^2-4)	\int\:_{0}^{7}(x^{2}-4)dx
integral from 3 to u of 1/(x+x^2)	\int\:_{3}^{u}\frac{1}{x+x^{2}}dx
integral from 1 to 9 of (x-6)/(sqrt(x))	\int\:_{1}^{9}\frac{x-6}{\sqrt{x}}dx
integral from-pi to pi of xsin(kx)	\int\:_{-π}^{π}x\sin(kx)dx
integral from 0 to 5 of x(3)	\int\:_{0}^{5}x(3)dx
integral from-1 to 3 of (x^3-1)	\int\:_{-1}^{3}(x^{3}-1)dx
integral from 0 to 2pi of 6cos^2(x)	\int\:_{0}^{2π}6\cos^{2}(x)dx
integral from 6 to 36 of 1/(x(ln(x))^8)	\int\:_{6}^{36}\frac{1}{x(\ln(x))^{8}}dx
integral from 1 to e^x of 9ln(x)	\int\:_{1}^{e^{x}}9\ln(x)dx
integral from 3 to 5 of 1/(sqrt(x-4))	\int\:_{3}^{5}\frac{1}{\sqrt{x-4}}dx
integral from 0 to 1 of 5x(1-x)^4	\int\:_{0}^{1}5x(1-x)^{4}dx
integral from 0 to 1 of ax+b	\int\:_{0}^{1}ax+bdx
integral from-1 to 1 of sec^3(x)tan^3(x)	\int\:_{-1}^{1}\sec^{3}(x)\tan^{3}(x)dx
integral from 0 to (3pi)/4 of tan(x/3)	\int\:_{0}^{\frac{3π}{4}}\tan(\frac{x}{3})dx
integral from-2 to 1 of (5x^2-7x+3)	\int\:_{-2}^{1}(5x^{2}-7x+3)dx
integral from-1 to 4 of (3x^4-4x^3-x-4)	\int\:_{-1}^{4}(3x^{4}-4x^{3}-x-4)dx
integral from 0 to 2 of (6x-6)(8x^2+2)	\int\:_{0}^{2}(6x-6)(8x^{2}+2)dx
integral from 1 to 12 of 4/(x^2)ln(x)	\int\:_{1}^{12}\frac{4}{x^{2}}\ln(x)dx
integral from-7 to 8 of x	\int\:_{-7}^{8}xdx
integral from 0 to 1 of e^{5x}-e^{4x}	\int\:_{0}^{1}e^{5x}-e^{4x}dx
integral from 0 to infinity of tan(x)	\int\:_{0}^{\infty\:}\tan(x)dx
integral from 2 to 4 of (x^2-4)/(x^2)	\int\:_{2}^{4}\frac{x^{2}-4}{x^{2}}dx
integral from 0 to 2 of (2x-9)(4x^2+4)	\int\:_{0}^{2}(2x-9)(4x^{2}+4)dx
integral from 0 to 1 of e^x-x^2	\int\:_{0}^{1}e^{x}-x^{2}dx
integral from 0 to 1 of 1000*2^t	\int\:_{0}^{1}1000\cdot\:2^{t}dt
integral from 0 to 2 of x/(1+6x^2)	\int\:_{0}^{2}\frac{x}{1+6x^{2}}dx
integral from 0 to pi/4 of (sec(x))^3	\int\:_{0}^{\frac{π}{4}}(\sec(x))^{3}dx
integral from 1 to 2 of 3x^3-9x^2+6x	\int\:_{1}^{2}3x^{3}-9x^{2}+6xdx
integral from 0 to 1 of x(1-x^2)^9	\int\:_{0}^{1}x(1-x^{2})^{9}dx
integral from 0 to 3 of 400-20t	\int\:_{0}^{3}400-20tdt
integral from 1.4 to 1.9 of 1/2 x	\int\:_{1.4}^{1.9}\frac{1}{2}xdx
integral from 4 to 8 of 6x	\int\:_{4}^{8}6xdx
integral from 1 to-1 of x^3	\int\:_{1}^{-1}x^{3}dx
integral from 0 to 5 of 2/(x+1)	\int\:_{0}^{5}\frac{2}{x+1}dx
integral from 5 to 6 of 2log_{10}(x)	\int\:_{5}^{6}2\log_{10}(x)dx
integral from 1 to 10 of x^2-x	\int\:_{1}^{10}x^{2}-xdx
integral from 0 to 9 of sqrt(8t)	\int\:_{0}^{9}\sqrt{8t}dt
integral from 0 to 1 of ln(x)x	\int\:_{0}^{1}\ln(x)xdx
integral from 2 to 6 of 7	\int\:_{2}^{6}7dx
integral from 1 to 5 of (ln(r))/(r^2)	\int\:_{1}^{5}\frac{\ln(r)}{r^{2}}dr
integral from x^3 to 8 of 2xy	\int\:_{x^{3}}^{8}2xydy
integral from 0 to sqrt((4-x^2) of)y	\int\:_{0}^{\sqrt{(4-x^{2})}}ydy
integral from 0 to 6 of-3x^2-12x+180	\int\:_{0}^{6}-3x^{2}-12x+180dx
integral from 0 to 1 of 2x^3e^{-x^2}	\int\:_{0}^{1}2x^{3}e^{-x^{2}}dx
integral from-pi to pi of cos^2(k)x	\int\:_{-π}^{π}\cos^{2}(k)xdx
integral from 1 to 10 of (5/x)	\int\:_{1}^{10}(\frac{5}{x})dx
integral from 0 to 1 of 4y^2(1-y^2)	\int\:_{0}^{1}4y^{2}(1-y^{2})dy
integral from 1 to infinity of 7/(x^2)	\int\:_{1}^{\infty\:}\frac{7}{x^{2}}dx
integral from 4 to 1 of 1	\int\:_{4}^{1}1
integral from-2 to 0 of-sin((npix)/2)	\int\:_{-2}^{0}-\sin(\frac{nπx}{2})dx
integral from 4 to 3 of 1	\int\:_{4}^{3}1
integral from 4 to 8 of (sqrt(x^2-16))/x	\int\:_{4}^{8}\frac{\sqrt{x^{2}-16}}{x}dx
integral from 0 to 4 of pisqrt(x)	\int\:_{0}^{4}π\sqrt{x}dx
integral from 5x to x^4 of e^{-t^2}	\int\:_{5x}^{x^{4}}e^{-t^{2}}dt
integral from 0 to 1 of 3te^{8t^2}	\int\:_{0}^{1}3te^{8t^{2}}dt
integral from-infinity to-3 of 2/(x+2)	\int\:_{-\infty\:}^{-3}\frac{2}{x+2}dx

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