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Popular Calculus Problems

integral from 0 to 3 of cos(pix)	\int\:_{0}^{3}\cos(πx)dx
integral from 0 to r of (r-(r^3)/(r^2))	\int\:_{0}^{r}(r-\frac{r^{3}}{r^{2}})dr
integral from 0 to pi of sqrt(sin^3(x))	\int\:_{0}^{π}\sqrt{\sin^{3}(x)}dx
integral from-1 to 2 of 5x^2	\int\:_{-1}^{2}5x^{2}dx
integral from 2 to 4 of y^2	\int\:_{2}^{4}y^{2}dy
integral from x^2 to 8-x^2 of y^2-x^2	\int\:_{x^{2}}^{8-x^{2}}y^{2}-x^{2}dy
integral from pi/2 to pi of (x-sin(x))	\int\:_{\frac{π}{2}}^{π}(x-\sin(x))dx
integral from-1/2 to 5/4 of x^3	\int\:_{-\frac{1}{2}}^{\frac{5}{4}}x^{3}dx
integral from 0 to 1 of (e^x-1)/(e^x+1)	\int\:_{0}^{1}\frac{e^{x}-1}{e^{x}+1}dx
integral from 2 to 1 of y^2-9	\int\:_{2}^{1}y^{2}-9dy
integral from 0 to 1.5 of 3/(2w^2)	\int\:_{0}^{1.5}\frac{3}{2w^{2}}dw
integral from 0 to 3 of 1/(x^2+16)	\int\:_{0}^{3}\frac{1}{x^{2}+16}dx
integral from-1 to 1 of (4x^2+1)	\int\:_{-1}^{1}(4x^{2}+1)dx
integral from-pi/2 to pi/2 of 648cos(x)	\int\:_{-\frac{π}{2}}^{\frac{π}{2}}648\cos(x)dx
integral from pi/2 to pi of sin^4(x)	\int\:_{\frac{π}{2}}^{π}\sin^{4}(x)dx
integral from 0 to 5 of w/(w^2-2)	\int\:_{0}^{5}\frac{w}{w^{2}-2}dw
integral from-1 to 2 of x+3-(x^2+1)	\int\:_{-1}^{2}x+3-(x^{2}+1)dx
integral from 0 to 2-x of 3/4 y	\int\:_{0}^{2-x}\frac{3}{4}ydy
integral from 0 to 2 of (x-3)^2	\int\:_{0}^{2}(x-3)^{2}dx
integral from 0 to 6 of 3x^2-24x+45	\int\:_{0}^{6}3x^{2}-24x+45dx
integral from 0 to (5pi)/4 of sec^4(t/5)	\int\:_{0}^{\frac{5π}{4}}\sec^{4}(\frac{t}{5})dt
integral from x to 2-x^2 of 1	\int\:_{x}^{2-x^{2}}1dy
integral from 1 to 2 of (2^{ln(x)})/x	\int\:_{1}^{2}\frac{2^{\ln(x)}}{x}dx
integral from 1 to 3 of (8x^3+6x-45)	\int\:_{1}^{3}(8x^{3}+6x-45)dx
integral from 0 to 1 of (2e^{3x})/7	\int\:_{0}^{1}\frac{2e^{3x}}{7}dx
integral from 0 to a of (bcos(cx)+	\int\:_{0}^{a}(b\cos(cx)+d)dx
integral from 2 to 3 of 1/(x^3+2x)	\int\:_{2}^{3}\frac{1}{x^{3}+2x}dx
integral from-2 to 2 of (3xy^2)/(x^2+1)	\int\:_{-2}^{2}\frac{3xy^{2}}{x^{2}+1}dy
integral from 1 to 3 of sin(r^2)r	\int\:_{1}^{3}\sin(r^{2})rdr
integral from 0 to 1 of (1/(x+2))	\int\:_{0}^{1}(\frac{1}{x+2})dx
integral from x to 1 of ysqrt(1+x^2-y^2)	\int\:_{x}^{1}y\sqrt{1+x^{2}-y^{2}}dy
integral from 0 to infinity of xe^{-θx}	\int\:_{0}^{\infty\:}xe^{-θx}dx
integral from 1 to 2 of (1-x^2)	\int\:_{1}^{2}(1-x^{2})dx
integral from 0 to pi of sin^4(t)	\int\:_{0}^{π}\sin^{4}(t)dt
integral from-1 to 0 of 3t^2e^{(-t^3+1)}	\int\:_{-1}^{0}3t^{2}e^{(-t^{3}+1)}dt
integral from-1 to 1 of x-2	\int\:_{-1}^{1}x-2dx
integral from 5 to 10 of (5x-2)/(x^2-4)	\int\:_{5}^{10}\frac{5x-2}{x^{2}-4}dx
integral from-2 to 1 of (5z^2-7z+z)	\int\:_{-2}^{1}(5z^{2}-7z+z)dz
integral from 0 to infinity of 4xye^{-(x^2+y^2)}	\int\:_{0}^{\infty\:}4xye^{-(x^{2}+y^{2})}dy
integral from 1 to x of 3t^{-4}	\int\:_{1}^{x}3t^{-4}dt
integral from 0 to infinity of e^{-2bx}	\int\:_{0}^{\infty\:}e^{-2bx}dx
integral from-2 to-1 of 4y^3+2/(y^3)	\int\:_{-2}^{-1}4y^{3}+\frac{2}{y^{3}}dy
integral from-1 to 2 of (3/2)^{x^2}	\int\:_{-1}^{2}(\frac{3}{2})^{x^{2}}dx
integral from 2 to 3 of 5x^4-8x^3+1	\int\:_{2}^{3}5x^{4}-8x^{3}+1dx
integral from 0 to 1 of-2x+3	\int\:_{0}^{1}-2x+3dx
integral from 0 to 1 of sqrt(4-y^2)	\int\:_{0}^{1}\sqrt{4-y^{2}}dy
integral from 1 to 3 of \sqrt[3]{x^2}	\int\:_{1}^{3}\sqrt[3]{x^{2}}dx
integral from 1 to e of (-3/x+2)	\int\:_{1}^{e}(-\frac{3}{x}+2)dx
integral from-a to a of (a^2-x^2)^2	\int\:_{-a}^{a}(a^{2}-x^{2})^{2}dx
integral from-2 to-1 of 1+x^3	\int\:_{-2}^{-1}1+x^{3}dx
integral from-1 to 1 of x^4-1	\int\:_{-1}^{1}x^{4}-1dx
integral from 4x to 4 of e^{-y^2}	\int\:_{4x}^{4}e^{-y^{2}}dy
integral from 3 to 3.5 of 2x^2	\int\:_{3}^{3.5}2x^{2}dx
integral from-pi to 0 of-picos(nx)	\int\:_{-π}^{0}-π\cos(nx)dx
integral from 0 to pi of 1-cos(θ)	\int\:_{0}^{π}1-\cos(θ)dθ
integral from-pi/4 to pi/2 of cos(x)	\int\:_{-\frac{π}{4}}^{\frac{π}{2}}\cos(x)dx
integral from-1 to 1 of 9	\int\:_{-1}^{1}9dx
integral from 1 to 3 of (2x+1/x)	\int\:_{1}^{3}(2x+\frac{1}{x})dx
integral from 0 to 8 of xsqrt(8-x)	\int\:_{0}^{8}x\sqrt{8-x}dx
integral from 2 to 6 of (x^2-4)	\int\:_{2}^{6}(x^{2}-4)dx
integral from 0 to pi/2 of θarctan(θ)	\int\:_{0}^{\frac{π}{2}}θ\arctan(θ)dθ
integral from 0 to 3 of x*(2x)/9	\int\:_{0}^{3}x\cdot\:\frac{2x}{9}dx
integral from 0 to 1 of (3x)/(x^2+1)	\int\:_{0}^{1}\frac{3x}{x^{2}+1}dx
integral from 0 to pi/4 of (tan(x))^4	\int\:_{0}^{\frac{π}{4}}(\tan(x))^{4}dx
integral from 1 to 4 of sin(x)	\int\:_{1}^{4}\sin(x)dx
integral from-125 to 125 of 1/(x^{1/3)}	\int\:_{-125}^{125}\frac{1}{x^{\frac{1}{3}}}dx
integral from 0 to 6 of x^2-5x	\int\:_{0}^{6}x^{2}-5xdx
integral from 0 to 1/2 of (2x^2+x)	\int\:_{0}^{\frac{1}{2}}(2x^{2}+x)dx
integral from-1 to 3 of sqrt(1+(2)^2)	\int\:_{-1}^{3}\sqrt{1+(2)^{2}}dx
integral from 0 to 3 of (x^3-x^2-6x)	\int\:_{0}^{3}(x^{3}-x^{2}-6x)dx
integral from-3 to-2 of (x^5)/4-x^2+3	\int\:_{-3}^{-2}\frac{x^{5}}{4}-x^{2}+3dx
integral from pi/2 to (3pi)/2 of cos(θ)	\int\:_{\frac{π}{2}}^{\frac{3π}{2}}\cos(θ)dθ
integral from 0 to 5 of 15x^3-2	\int\:_{0}^{5}15x^{3}-2dx
integral from 0 to 5 of (10x+7)	\int\:_{0}^{5}(10x+7)dx
integral from 1/4 to 1/2 of x	\int\:_{\frac{1}{4}}^{\frac{1}{2}}xdx
integral from 0 to 27 of \sqrt[3]{x}-1/x	\int\:_{0}^{27}\sqrt[3]{x}-\frac{1}{x}dx
integral from-pi to pi of sin^2(x)cos(x)	\int\:_{-π}^{π}\sin^{2}(x)\cos(x)dx
integral from 4 to 6 of x/(x-3)	\int\:_{4}^{6}\frac{x}{x-3}dx
integral from 0 to 2 of sqrt(1+(2x-2)^2)	\int\:_{0}^{2}\sqrt{1+(2x-2)^{2}}dx
integral from 0 to pi/2 of e^{-t}sin(t)	\int\:_{0}^{\frac{π}{2}}e^{-t}\sin(t)dt
integral from e^3 to e^6 of ln(x)	\int\:_{e^{3}}^{e^{6}}\ln(x)dx
integral from 1 to 4 of x+1/x	\int\:_{1}^{4}x+\frac{1}{x}dx
integral from-infinity to 0 of xe^{ax}	\int\:_{-\infty\:}^{0}xe^{ax}dx
integral from 0 to pi of x^3cos(2x)	\int\:_{0}^{π}x^{3}\cos(2x)dx
integral from 2 to infinity of x^{-1/3}	\int\:_{2}^{\infty\:}x^{-\frac{1}{3}}dx
integral from-1 to 2 of (-x^4-x^2+6x+8)	\int\:_{-1}^{2}(-x^{4}-x^{2}+6x+8)dx
integral from 0 to 2pi of sin(2x)sin(3x)	\int\:_{0}^{2π}\sin(2x)\sin(3x)dx
integral from 0 to 2 of 7x^4	\int\:_{0}^{2}7x^{4}dx
integral from 0 to pi of cos^2(x)sin(2x)	\int\:_{0}^{π}\cos^{2}(x)\sin(2x)dx
integral from 2 to 6 of-(x^2-7x+6)	\int\:_{2}^{6}-(x^{2}-7x+6)dx
integral from 0 to infinity of 12e^{-2x}	\int\:_{0}^{\infty\:}12e^{-2x}dx
integral from 3 to 5 of e^{2-x}	\int\:_{3}^{5}e^{2-x}dx
integral from-infinity to-5 of θe^θ	\int\:_{-\infty\:}^{-5}θe^{θ}dθ
integral from 0 to 1.5 of 1/8 x	\int\:_{0}^{1.5}\frac{1}{8}xdx
integral from 0 to 1 of 2cos(x)	\int\:_{0}^{1}2\cos(x)dx
integral from 9 to 10 of 1.5x^{-2.5}	\int\:_{9}^{10}1.5x^{-2.5}dx
integral from 2 to 4 of-6x	\int\:_{2}^{4}-6xdx
integral from 0 to 2pi of 2cos(2x+4)	\int\:_{0}^{2π}2\cos(2x+4)dx
integral from 0 to 1 of xsqrt(4x-x^2)	\int\:_{0}^{1}x\sqrt{4x-x^{2}}dx
integral from 100 to 150 of-6x^2+20x	\int\:_{100}^{150}-6x^{2}+20xdx

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