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Popular Calculus Problems

limit as x approaches 0 of (1-4x)^{3/x}	\lim\:_{x\to\:0}((1-4x)^{\frac{3}{x}})
derivative of-e^{-x}	\frac{d}{dx}(-e^{-x})
(dy)/(dx)=5y+3	\frac{dy}{dx}=5y+3
derivative of f(x)=(4x^5-5x^4)	derivative\:f(x)=(4x^{5}-5x^{4})
integral of e^{sqrt(5x)}	\int\:e^{\sqrt{5x}}dx
integral of (x^2)/(sqrt(x)+1)	\int\:\frac{x^{2}}{\sqrt{x}+1}dx
integral of (x^2-1)sqrt(2x+1)	\int\:(x^{2}-1)\sqrt{2x+1}dx
derivative of 15x^2-15x^4	\frac{d}{dx}(15x^{2}-15x^{4})
integral of 1/((x-6)^2)	\int\:\frac{1}{(x-6)^{2}}dx
derivative of f(x)=(1+csc(x^3))/(1-cot(x^3))	derivative\:f(x)=\frac{1+\csc(x^{3})}{1-\cot(x^{3})}
d/(dt)(-4t^2+176t+100)	\frac{d}{dt}(-4t^{2}+176t+100)
(\partial)/(\partial z)(2y)	\frac{\partial\:}{\partial\:z}(2y)
(\partial)/(\partial x)(2y-2yx)	\frac{\partial\:}{\partial\:x}(2y-2yx)
derivative of 3ln(sin(x))	\frac{d}{dx}(3\ln(\sin(x)))
derivative of 1/4	derivative\:\frac{1}{4}
integral of (cos(5x))^2	\int\:(\cos(5x))^{2}dx
taylor sin(pi/2-x)	taylor\:\sin(\frac{π}{2}-x)
limit as x approaches-1-of x^2	\lim\:_{x\to\:-1-}(x^{2})
limit as x approaches 3-of (x^2)/(x-3)	\lim\:_{x\to\:3-}(\frac{x^{2}}{x-3})
integral of e^{(a-s)x}	\int\:e^{(a-s)x}dx
integral of (6x^2+2x-1)/(3x^2)	\int\:\frac{6x^{2}+2x-1}{3x^{2}}dx
derivative of y/(x^2+y^2+1)	\frac{d}{dx}(\frac{y}{x^{2}+y^{2}+1})
derivative of ln(xsec(x))	\frac{d}{dx}(\ln(x)\sec(x))
(dy)/(dx)=3x^2-xy	\frac{dy}{dx}=3x^{2}-xy
integral of x^6cos(x)	\int\:x^{6}\cos(x)dx
derivative of ln(cos(5x))	derivative\:\ln(\cos(5x))
(\partial)/(\partial x)((e^{x^2}+e^{y^2})^2)	\frac{\partial\:}{\partial\:x}((e^{x^{2}}+e^{y^{2}})^{2})
integral of 1/(sin(x/2))	\int\:\frac{1}{\sin(\frac{x}{2})}dx
integral of x^2ln(100)	\int\:x^{2}\ln(100)dx
derivative of ln(sqrt(4-x^2))	derivative\:\ln(\sqrt{4-x^{2}})
integral of (1-cos^2(x))/(sin(x))	\int\:\frac{1-\cos^{2}(x)}{\sin(x)}dx
y^'=2x+y	y^{\prime\:}=2x+y
derivative of (10)/(ln(x))	derivative\:\frac{10}{\ln(x)}
area 16-x^2,x^2-2,-3,3	area\:16-x^{2},x^{2}-2,-3,3
derivative of f(x)=log_{9}(x)	derivative\:f(x)=\log_{9}(x)
derivative of 4/3 x^3-4x^2-60x+10	\frac{d}{dx}(\frac{4}{3}x^{3}-4x^{2}-60x+10)
area x^{1/4},sqrt(2-x),0	area\:x^{\frac{1}{4}},\sqrt{2-x},0
tangent of f(x)=x^3-3x^2+1,\at x=2	tangent\:f(x)=x^{3}-3x^{2}+1,\at\:x=2
integral of (ln(ln(x)))/x	\int\:\frac{\ln(\ln(x))}{x}dx
roots pir^2h	roots\:πr^{2}h
integral of x^3-4x	\int\:x^{3}-4xdx
integral of sin^9(x)cos^5(x)	\int\:\sin^{9}(x)\cos^{5}(x)dx
derivative of \sqrt[3]{x^2-1}	\frac{d}{dx}(\sqrt[3]{x^{2}-1})
(dy)/(dx)= x/(y^2)	\frac{dy}{dx}=\frac{x}{y^{2}}
integral of (x^2+3)^2	\int\:(x^{2}+3)^{2}dx
derivative of 6x^{2/3}	derivative\:6x^{\frac{2}{3}}
integral of e^{-5r}	\int\:e^{-5r}dr
derivative of y=e^{2x-x^2}	derivative\:y=e^{2x-x^{2}}
(dy)/(dx)=(8x)/(7y)	\frac{dy}{dx}=\frac{8x}{7y}
integral of ln((1+x)/(1-x))	\int\:\ln(\frac{1+x}{1-x})dx
tangent of (3x+28)^{1/2}	tangent\:(3x+28)^{\frac{1}{2}}
integral of e^{y/(sqrt(x))}	\int\:e^{\frac{y}{\sqrt{x}}}dy
tangent of f(x)=9-ln(x),\at x=1	tangent\:f(x)=9-\ln(x),\at\:x=1
integral of 1/(xsqrt(25x^2+1))	\int\:\frac{1}{x\sqrt{25x^{2}+1}}dx
integral of (-y^2+1)-(2y^2-2)	\int\:(-y^{2}+1)-(2y^{2}-2)dy
derivative of sec^6(x)	derivative\:\sec^{6}(x)
t(dy)/(dt)=t^3+12t^3y	t\frac{dy}{dt}=t^{3}+12t^{3}y
integral of x^2-sqrt(x)	\int\:x^{2}-\sqrt{x}dx
derivative of f(x)=ln(x+ln(x))	derivative\:f(x)=\ln(x+\ln(x))
derivative of-1/(1-x)	derivative\:-\frac{1}{1-x}
(\partial)/(\partial x)(2e^yxy)	\frac{\partial\:}{\partial\:x}(2e^{y}xy)
tangent of f(x)=-3x^{2/3},\at x=-8	tangent\:f(x)=-3x^{\frac{2}{3}},\at\:x=-8
limit as x approaches+0 of x^x	\lim\:_{x\to\:+0}(x^{x})
integral of y^{-1}	\int\:y^{-1}dy
integral from-1 to 1 of x^2-x^4	\int\:_{-1}^{1}x^{2}-x^{4}dx
derivative of 4(e^x^9)	\frac{d}{dx}(4(e^{x})^{9})
inverse oflaplace (s+2)/((s+1)(s-s^2))	inverselaplace\:\frac{s+2}{(s+1)(s-s^{2})}
integral of (8x^2-4x+7)/(4x^3+x^2+4x+1)	\int\:\frac{8x^{2}-4x+7}{4x^{3}+x^{2}+4x+1}dx
tangent of f(x)=-x^2-4x+2,\at x=-1	tangent\:f(x)=-x^{2}-4x+2,\at\:x=-1
derivative of (x^2-36/(x+6))	\frac{d}{dx}(\frac{x^{2}-36}{x+6})
derivative of 3^{x+10}	\frac{d}{dx}(3^{x+10})
integral of 1/(sqrt(x)(x+2))	\int\:\frac{1}{\sqrt{x}(x+2)}dx
(2y+2t-7)dt+(4y+2t-1)dy=0	(2y+2t-7)dt+(4y+2t-1)dy=0
integral of 1/((16-x^2)^2)	\int\:\frac{1}{(16-x^{2})^{2}}dx
derivative of sin^2(e^{sin^2(x)})	derivative\:\sin^{2}(e^{\sin^{2}(x)})
derivative of (2x/9)	\frac{d}{dx}(\frac{2x}{9})
integral of e^{0.1x}	\int\:e^{0.1x}dx
integral of sqrt(cos^2(x)+1)	\int\:\sqrt{\cos^{2}(x)+1}dx
integral from 0 to (1-u)/4 of 2(1-y)	\int\:_{0}^{\frac{1-u}{4}}2(1-y)dy
integral from 0 to 1 of e^x(4-e^x)	\int\:_{0}^{1}e^{x}(4-e^{x})dx
sum from n=1 to infinity of-1/2	\sum\:_{n=1}^{\infty\:}-\frac{1}{2}
integral of ((x^2))/(sqrt(25-x^2))	\int\:\frac{(x^{2})}{\sqrt{25-x^{2}}}dx
yln(x)((dy}{dx})=(\frac{y+1)/x)^2	y\ln(x)(\frac{dy}{dx})=(\frac{y+1}{x})^{2}
integral from 1 to 9 of x^2	\int\:_{1}^{9}x^{2}dx
integral of 6cos^4(x)	\int\:6\cos^{4}(x)dx
laplacetransform f(k)ke^{-3k}	laplacetransform\:f(k)ke^{-3k}
parity y=x^{3sin(x)}	parity\:y=x^{3\sin(x)}
integral of (sqrt(400-x^2))/x	\int\:\frac{\sqrt{400-x^{2}}}{x}dx
(\partial)/(\partial x)(ln(x)+y^3x)	\frac{\partial\:}{\partial\:x}(\ln(x)+y^{3}x)
(\partial)/(\partial x)(x^3+sin(xy))	\frac{\partial\:}{\partial\:x}(x^{3}+\sin(xy))
integral from 2 to 6 of x/(sqrt(2x-3))	\int\:_{2}^{6}\frac{x}{\sqrt{2x-3}}dx
integral of cos(5x+1)	\int\:\cos(5x+1)dx
integral of 3/(18+2x^2)	\int\:\frac{3}{18+2x^{2}}dx
integral from-2 to 1 of 0	\int\:_{-2}^{1}0dx
integral from 0 to 4 of (4-x)^2	\int\:_{0}^{4}(4-x)^{2}dx
y^{''}-(2/x)y^'-(3/(x^2))y=0	y^{\prime\:\prime\:}-(\frac{2}{x})y^{\prime\:}-(\frac{3}{x^{2}})y=0
sum from n=0 to infinity of cos(2n)	\sum\:_{n=0}^{\infty\:}\cos(2n)
limit as r approaches 1 of sqrt((8r+1)/(r+3))	\lim\:_{r\to\:1}(\sqrt{\frac{8r+1}{r+3}})
derivative of 4x^3-48x^2+6x+4	derivative\:4x^{3}-48x^{2}+6x+4
e^x(dy)/(dx)+xy^2=0	e^{x}\frac{dy}{dx}+xy^{2}=0

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