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Popular Calculus Problems

integral of (x^{10}+10^x)/(10)	\int\:\frac{x^{10}+10^{x}}{10}dx
sum from n=0 to infinity of 2/(n^2+1)	\sum\:_{n=0}^{\infty\:}\frac{2}{n^{2}+1}
limit as x approaches 3 of (4x-4)/(5x-1)	\lim\:_{x\to\:3}(\frac{4x-4}{5x-1})
derivative of (5x/(sqrt(x^2+7)))	\frac{d}{dx}(\frac{5x}{\sqrt{x^{2}+7}})
limit as x approaches 0 of x/(2x)	\lim\:_{x\to\:0}(\frac{x}{2x})
integral from 0 to pi/6 of sqrt(1-cos(6x))	\int\:_{0}^{\frac{π}{6}}\sqrt{1-\cos(6x)}dx
limit as x approaches 0 of (1+7x)^{1/x}	\lim\:_{x\to\:0}((1+7x)^{\frac{1}{x}})
integral of ((y+1))/(y^2+y+1)	\int\:\frac{(y+1)}{y^{2}+y+1}dy
derivative of y=\sqrt[3]{1+5x}	derivative\:y=\sqrt[3]{1+5x}
integral of (5+x+x^2)/(sqrt(x))	\int\:\frac{5+x+x^{2}}{\sqrt{x}}dx
integral of (2x+11)/(x^2+4x+5)	\int\:\frac{2x+11}{x^{2}+4x+5}dx
(\partial)/(\partial x)(8x^2y-3)	\frac{\partial\:}{\partial\:x}(8x^{2}y-3)
limit as x approaches-2 of-x^2-4x	\lim\:_{x\to\:-2}(-x^{2}-4x)
integral from 0 to 1 of (2x)	\int\:_{0}^{1}(2x)dx
derivative of (4x-9)/(x-9)	derivative\:\frac{4x-9}{x-9}
limit as x approaches 0-of x^2+1/x	\lim\:_{x\to\:0-}(x^{2}+\frac{1}{x})
maclaurin 2/(1-x^2)	maclaurin\:\frac{2}{1-x^{2}}
integral of 1/(4e^{-6x)+e^{6x}}	\int\:\frac{1}{4e^{-6x}+e^{6x}}dx
derivative of g(t)= 3/(t^2)	derivative\:g(t)=\frac{3}{t^{2}}
limit as x approaches 2 of 5x+3	\lim\:_{x\to\:2}(5x+3)
(dy)/(dx)=x	\frac{dy}{dx}=x
integral of cos^4(x)-cos^6(x)	\int\:\cos^{4}(x)-\cos^{6}(x)dx
(\partial)/(\partial y)(e^x+cos(y))	\frac{\partial\:}{\partial\:y}(e^{x}+\cos(y))
derivative of ln(8)	derivative\:\ln(8)
integral of 1/(xln(x)-x)	\int\:\frac{1}{x\ln(x)-x}dx
(\partial)/(\partial x)(xe^y-e^z)	\frac{\partial\:}{\partial\:x}(xe^{y}-e^{z})
implicit (dy)/(dx),ye^x=y	implicit\:\frac{dy}{dx},ye^{x}=y
derivative of (3x+1((x^2+4))/((6x-5)))	\frac{d}{dx}((3x+1)\frac{(x^{2}+4)}{(6x-5)})
integral of (sin(2x))/(sin(x))	\int\:\frac{\sin(2x)}{\sin(x)}dx
derivative of y=2csc(8x^3-8x+8)	derivative\:y=2\csc(8x^{3}-8x+8)
integral from 0 to 1 of 8cos(4x)	\int\:_{0}^{1}8\cos(4x)dx
integral of tan^3(x)sec^5(x)	\int\:\tan^{3}(x)\sec^{5}(x)dx
(\partial)/(\partial x)((1-ln(x))/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{1-\ln(x)}{x^{2}})
(\partial)/(\partial x)(ln(9x))	\frac{\partial\:}{\partial\:x}(\ln(9x))
derivative of 4/(7x^4)	\frac{d}{dx}(\frac{4}{7x^{4}})
y^'+sin(t)y=sin(t),y(0)=7	y^{\prime\:}+\sin(t)y=\sin(t),y(0)=7
tangent of y=x^2+9x,\at x=-8	tangent\:y=x^{2}+9x,\at\:x=-8
derivative of-cos(e^x)	\frac{d}{dx}(-\cos(e^{x}))
integral from 1 to 6 of 1/(2sqrt(x+3)+x)	\int\:_{1}^{6}\frac{1}{2\sqrt{x+3}+x}dx
derivative of 7sqrt(x)(x^3-8sqrt(x)+2)	\frac{d}{dx}(7\sqrt{x}(x^{3}-8\sqrt{x}+2))
x(dy)/(dx)-2y=5x^3	x\frac{dy}{dx}-2y=5x^{3}
(\partial)/(\partial x)((x^2)/(sin^2(x)))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{\sin^{2}(x)})
(\partial)/(\partial z)(((x+y))/(y+z))	\frac{\partial\:}{\partial\:z}(\frac{(x+y)}{y+z})
limit as x approaches 2+of-5/(x-2)	\lim\:_{x\to\:2+}(-\frac{5}{x-2})
integral from 4 to-4 of (-7)	\int\:_{4}^{-4}(-7)dx
laplacetransform t^2+e^{-t}sin(2t)	laplacetransform\:t^{2}+e^{-t}\sin(2t)
integral of-e^{-3x}	\int\:-e^{-3x}dx
integral of (e^{2x})/x	\int\:\frac{e^{2x}}{x}dx
integral of (3-x^2)*2^x	\int\:(3-x^{2})\cdot\:2^{x}dx
y^{''}+7y^'+12y=0,y(0)=a,y^'(0)=b	y^{\prime\:\prime\:}+7y^{\prime\:}+12y=0,y(0)=a,y^{\prime\:}(0)=b
integral from-1 to 2 of x^4	\int\:_{-1}^{2}x^{4}dx
limit as n approaches infinity of Dn	\lim\:_{n\to\:\infty\:}(Dn)
integral of cos^6(x)tan^3(x)	\int\:\cos^{6}(x)\tan^{3}(x)dx
(\partial)/(\partial x)(sec(x)tan(y))	\frac{\partial\:}{\partial\:x}(\sec(x)\tan(y))
integral of cos^2(x)+sin^2(x)	\int\:\cos^{2}(x)+\sin^{2}(x)dx
2y^'+1/x y=x^2y^{-1}	2y^{\prime\:}+\frac{1}{x}y=x^{2}y^{-1}
laplacetransform (1-cos(2(3t)))/2	laplacetransform\:\frac{1-\cos(2(3t))}{2}
limit as x approaches 0 of ((2^x-7^x))/x	\lim\:_{x\to\:0}(\frac{(2^{x}-7^{x})}{x})
inverse oflaplace 1/(s(s^2+2s+5))	inverselaplace\:\frac{1}{s(s^{2}+2s+5)}
derivative of 1/(y^2)-3/(y^4)	derivative\:\frac{1}{y^{2}}-\frac{3}{y^{4}}
(dy)/(dx)=e^{x-y}	\frac{dy}{dx}=e^{x-y}
tangent of f(x)=x^3ln(2x),\at x=1	tangent\:f(x)=x^{3}\ln(2x),\at\:x=1
integral from 1 to 9 of sqrt(y)ln(y)	\int\:_{1}^{9}\sqrt{y}\ln(y)dy
(\partial)/(\partial x)(x/(sin(2x+3y+z^2)))	\frac{\partial\:}{\partial\:x}(\frac{x}{\sin(2x+3y+z^{2})})
derivative of 6sqrt(4x^2+3)	derivative\:6\sqrt{4x^{2}+3}
(\partial)/(\partial u)(3vcos(u))	\frac{\partial\:}{\partial\:u}(3v\cos(u))
derivative of ln((x^2+4^5))	\frac{d}{dx}(\ln((x^{2}+4)^{5}))
limit as x approaches 4 of ((2))/(x-4)	\lim\:_{x\to\:4}(\frac{(2)}{x-4})
limit as x approaches 2-of (2x)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{2x}{x^{2}-4})
y^{''}+8y^'+25y=0,y(0)=3,y^'(0)=-10	y^{\prime\:\prime\:}+8y^{\prime\:}+25y=0,y(0)=3,y^{\prime\:}(0)=-10
limit as x approaches-2+of (-7x)/(x+2)	\lim\:_{x\to\:-2+}(\frac{-7x}{x+2})
integral of 7*tan^3(x)sec(x)	\int\:7\cdot\:\tan^{3}(x)\sec(x)dx
tangent of f(x)=4x^2+9x	tangent\:f(x)=4x^{2}+9x
integral of (6t-5)/(t+1)	\int\:\frac{6t-5}{t+1}dt
f(x)=5x^3	f(x)=5x^{3}
(1+x)dy=(y+x)dx	(1+x)dy=(y+x)dx
tangent of f(x)=x^2-x+2,\at x=1	tangent\:f(x)=x^{2}-x+2,\at\:x=1
integral from-pi to 0 of 0	\int\:_{-π}^{0}0dx
integral from 0 to 4 of 1/((9-3x)^{1/3)}	\int\:_{0}^{4}\frac{1}{(9-3x)^{\frac{1}{3}}}dx
integral of 3x^2+C	\int\:3x^{2}+Cdx
derivative of f(x)=3x+5/x	derivative\:f(x)=3x+\frac{5}{x}
limit as x approaches 3+of xsqrt(x-3)	\lim\:_{x\to\:3+}(x\sqrt{x-3})
xy^'+3y=(4e^{-3x})/(x^2)	xy^{\prime\:}+3y=\frac{4e^{-3x}}{x^{2}}
derivative of sqrt(x^2+4x)	\frac{d}{dx}(\sqrt{x^{2}+4x})
(dy}{dx}=\frac{2x(y+1))/y	\frac{dy}{dx}=\frac{2x(y+1)}{y}
derivative of 48	\frac{d}{dx}(48)
derivative of 2/(sqrt(4x+3))	\frac{d}{dx}(\frac{2}{\sqrt{4x+3}})
y^'+(x+3)y^2=0	y^{\prime\:}+(x+3)y^{2}=0
derivative of 7x^{1/3}-7x^{-2/3}	derivative\:7x^{\frac{1}{3}}-7x^{-\frac{2}{3}}
integral of 5/(sqrt(1-x^2))	\int\:\frac{5}{\sqrt{1-x^{2}}}dx
area y=x^3-5x,y=4x	area\:y=x^{3}-5x,y=4x
integral of (x^2+2x-3)/(x^4)	\int\:\frac{x^{2}+2x-3}{x^{4}}dx
derivative of-1x^{-3/5}	derivative\:-1x^{-\frac{3}{5}}
integral from 0 to y of 2e^{-x-y}	\int\:_{0}^{y}2e^{-x-y}dx
integral of cos(wt)	\int\:\cos(wt)dt
limit as x approaches-5 of (3x^2+15x)/(2x^2-50)	\lim\:_{x\to\:-5}(\frac{3x^{2}+15x}{2x^{2}-50})
derivative of y=(arctan(9x))^2	derivative\:y=(\arctan(9x))^{2}
integral of 3y^3	\int\:3y^{3}dy
derivative of (f(x(5x))^2-2)	\frac{d}{dx}((f(x)(5x))^{2}-2)
limit as x approaches 4 of (7x+6)/(3x-2)	\lim\:_{x\to\:4}(\frac{7x+6}{3x-2})

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