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Popular Calculus Problems

limit as x approaches 0 of 1+1/x	\lim\:_{x\to\:0}(1+\frac{1}{x})
integral of xe^{x^3}	\int\:xe^{x^{3}}dx
integral of sqrt(2x)-cos(6x)	\int\:\sqrt{2x}-\cos(6x)dx
(ye^{-2x}+y^3)dx-e^{-2x}dy=0	(ye^{-2x}+y^{3})dx-e^{-2x}dy=0
integral of 1/(sqrt(-x^2-x+2))	\int\:\frac{1}{\sqrt{-x^{2}-x+2}}dx
f(x)=e^{x^3+10x}	f(x)=e^{x^{3}+10x}
integral of 10x+2	\int\:10x+2dx
integral from 1/2 to 1 of (x^{-3}-5)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-5)dx
y^{''}=by	y^{\prime\:\prime\:}=by
integral from 1 to 2 of (x^2+5)/(3x-x^2)	\int\:_{1}^{2}\frac{x^{2}+5}{3x-x^{2}}dx
derivative of (x^2/(4+sqrt(x)))	\frac{d}{dx}(\frac{x^{2}}{4+\sqrt{x}})
integral from 0 to 3/4 of 60x	\int\:_{0}^{\frac{3}{4}}60xdx
y^'-3y+2x=0	y^{\prime\:}-3y+2x=0
limit as x approaches infinity of x^2-4	\lim\:_{x\to\:\infty\:}(x^{2}-4)
integral from 0 to 1 of y/(e^{7y)}	\int\:_{0}^{1}\frac{y}{e^{7y}}dy
derivative of (x^2+y^2^{4/5})	\frac{d}{dx}((x^{2}+y^{2})^{\frac{4}{5}})
integral of e^{3x}-1	\int\:e^{3x}-1dx
limit as x approaches infinity of e^x+e	\lim\:_{x\to\:\infty\:}(e^{x}+e)
derivative of sqrt(3x+\sqrt{x)}	\frac{d}{dx}(\sqrt{3x+\sqrt{x}})
derivative of (x^2+x/(x^2+4x))	\frac{d}{dx}(\frac{x^{2}+x}{x^{2}+4x})
derivative of ae^xcos(x+be^xsin(x))	\frac{d}{dx}(ae^{x}\cos(x)+be^{x}\sin(x))
derivative of \sqrt[4]{-3x^4-2}	\frac{d}{dx}(\sqrt[4]{-3x^{4}-2})
integral of (14x^2+9x+43)/((x+2)(x^2+5))	\int\:\frac{14x^{2}+9x+43}{(x+2)(x^{2}+5)}dx
integral of+sin^2(6x)cos^2(6x)	\int\:+\sin^{2}(6x)\cos^{2}(6x)dx
integral of [ 1/(x^2)+sec^2(pix)]	\int\:[\frac{1}{x^{2}}+\sec^{2}(πx)]dx
(\partial)/(\partial x)((xy)^{1/2})	\frac{\partial\:}{\partial\:x}((xy)^{\frac{1}{2}})
sum from n=8 to infinity of 1/(4^n)	\sum\:_{n=8}^{\infty\:}\frac{1}{4^{n}}
integral of (x^3)/((x+1)^3)	\int\:\frac{x^{3}}{(x+1)^{3}}dx
derivative of 2x(x+4^3)	\frac{d}{dx}(2x(x+4)^{3})
(\partial)/(\partial x)(x^2+3y^2-6y+4xy)	\frac{\partial\:}{\partial\:x}(x^{2}+3y^{2}-6y+4xy)
tangent of f(x)=-x^2+2x+4,\at x=3	tangent\:f(x)=-x^{2}+2x+4,\at\:x=3
derivative of y=-3x^2	derivative\:y=-3x^{2}
integral of 1/(-e^{2x)}	\int\:\frac{1}{-e^{2x}}dx
derivative of x+1/(x+1)	\frac{d}{dx}(x+\frac{1}{x+1})
tangent of f(x)= 1/(sqrt(x)),\at x=1	tangent\:f(x)=\frac{1}{\sqrt{x}},\at\:x=1
integral of e^{-t}cos(t)	\int\:e^{-t}\cos(t)dt
d/(dt)(1/2 e^{-4t}cos(8t))	\frac{d}{dt}(\frac{1}{2}e^{-4t}\cos(8t))
integral from 0 to 1 of pi(x^4-x)	\int\:_{0}^{1}π(x^{4}-x)dx
(\partial)/(\partial x)(e^{e^yx+y})	\frac{\partial\:}{\partial\:x}(e^{e^{y}x+y})
derivative of f(x)=4x^2+6x+3	derivative\:f(x)=4x^{2}+6x+3
integral of e^{-(x)^2}	\int\:e^{-(x)^{2}}dx
integral of 4xsin(5x)	\int\:4x\sin(5x)dx
integral of x^3sin(5x)	\int\:x^{3}\sin(5x)dx
integral of x*sin(x/2)	\int\:x\cdot\:\sin(\frac{x}{2})dx
tangent of 0.72x^3-4.8x^2+0.6x+7.6	tangent\:0.72x^{3}-4.8x^{2}+0.6x+7.6
integral from-1 to 1 of e^x-(x^2-2)	\int\:_{-1}^{1}e^{x}-(x^{2}-2)dx
(\partial)/(\partial x)((2x-y)/(x+2y))	\frac{\partial\:}{\partial\:x}(\frac{2x-y}{x+2y})
(\partial ^2)/(\partial x^2)(x^2-y^2)	\frac{\partial\:^{2}}{\partial\:x^{2}}(x^{2}-y^{2})
(\partial)/(\partial x)((4-x^2-y^2)^{1/2})	\frac{\partial\:}{\partial\:x}((4-x^{2}-y^{2})^{\frac{1}{2}})
d/(dt)(sqrt(1/(t^2-2)))	\frac{d}{dt}(\sqrt{\frac{1}{t^{2}-2}})
(\partial)/(\partial x)(ln(4+3x^2+2y^2))	\frac{\partial\:}{\partial\:x}(\ln(4+3x^{2}+2y^{2}))
derivative of f(x)=2sin^4(sqrt(x))	derivative\:f(x)=2\sin^{4}(\sqrt{x})
y^{''}-6y^'=-2x-5	y^{\prime\:\prime\:}-6y^{\prime\:}=-2x-5
derivative of (3x/y)	\frac{d}{dx}(\frac{3x}{y})
integral of (5x^4-4/(x^4))	\int\:(5x^{4}-\frac{4}{x^{4}})dx
tangent of y=(1-x)(x^2-3)^2,(2,-1)	tangent\:y=(1-x)(x^{2}-3)^{2},(2,-1)
taylor 1/(1-x),19	taylor\:\frac{1}{1-x},19
integral of x^2log_{3}(x)	\int\:x^{2}\log_{3}(x)dx
integral of x^2+e^x	\int\:x^{2}+e^{x}dx
tangent of y=(sqrt(x))/(8x-4),\at x=2	tangent\:y=\frac{\sqrt{x}}{8x-4},\at\:x=2
derivative of x^4-2	derivative\:x^{4}-2
tangent of-x^2+9x	tangent\:-x^{2}+9x
integral of 3e^{-x}sin(x)	\int\:3e^{-x}\sin(x)dx
inverse oflaplace (2s-4)/(s^2-4s+13)	inverselaplace\:\frac{2s-4}{s^{2}-4s+13}
derivative of-0.5x^2+64x-25	\frac{d}{dx}(-0.5x^{2}+64x-25)
y^{''}+y=3sin(x)	y^{\prime\:\prime\:}+y=3\sin(x)
y^{''}+y^'=6sin(2x)	y^{\prime\:\prime\:}+y^{\prime\:}=6\sin(2x)
limit as x approaches 8 of (5x-2)/(x+8)	\lim\:_{x\to\:8}(\frac{5x-2}{x+8})
integral from-2 to 2 of x^2sqrt(4-x^2)	\int\:_{-2}^{2}x^{2}\sqrt{4-x^{2}}dx
derivative of sqrt(5)x+sqrt(3x)	derivative\:\sqrt{5}x+\sqrt{3x}
limit as s approaches 1 of (s^3-1)/(s-1)	\lim\:_{s\to\:1}(\frac{s^{3}-1}{s-1})
limit as x approaches 6 of 5x	\lim\:_{x\to\:6}(5x)
integral from 0 to 2 of (x-1)^{25}	\int\:_{0}^{2}(x-1)^{25}dx
integral from-infinity to 0 of (xe^{2x})	\int\:_{-\infty\:}^{0}(xe^{2x})dx
derivative of cos^4(3x^2)	\frac{d}{dx}(\cos^{4}(3x^{2}))
sum from n=1 to infinity of 1/(n^2+n^3)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+n^{3}}
limit as x approaches 9 of sqrt(7x-8)	\lim\:_{x\to\:9}(\sqrt{7x-8})
(\partial)/(\partial x)(-2sqrt(\|x\|))	\frac{\partial\:}{\partial\:x}(-2\sqrt{\left\|x\right\|})
y^{''}-3y^'+2y=x^2	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=x^{2}
integral from-1 to 1 of (e^y-y^2+2)	\int\:_{-1}^{1}(e^{y}-y^{2}+2)dy
integral of (-6x^2)/(sqrt(4x-x^2))	\int\:\frac{-6x^{2}}{\sqrt{4x-x^{2}}}dx
derivative of f(X)=(X^3+3X+2)/(X^2-1)	derivative\:f(X)=\frac{X^{3}+3X+2}{X^{2}-1}
integral from-1 to-2 of (16-x^3)/(x^3)	\int\:_{-1}^{-2}\frac{16-x^{3}}{x^{3}}dx
integral of 5sin^3(5x)cos^3(5x)	\int\:5\sin^{3}(5x)\cos^{3}(5x)dx
(\partial)/(\partial x)(x^2y+e^{xy})	\frac{\partial\:}{\partial\:x}(x^{2}y+e^{xy})
(\partial ^3)/(\partial x\partial y\partial z)(e^{xyz^9})	\frac{\partial\:^{3}}{\partial\:x\partial\:y\partial\:z}(e^{xyz^{9}})
d/(dt)(sin(t))	\frac{d}{dt}(\sin(t))
3xy^'-15y=x^{-4},y(1)=-2	3xy^{\prime\:}-15y=x^{-4},y(1)=-2
integral from 0 to 4.5 of 90x	\int\:_{0}^{4.5}90xdx
derivative of 1+2tan(x)	\frac{d}{dx}(1+2\tan(x))
limit as x approaches 0 of x^2-1	\lim\:_{x\to\:0}(x^{2}-1)
integral of ln(x)sqrt(x^{15)}	\int\:\ln(x)\sqrt{x^{15}}dx
tangent of 3/((4x+1)^2)	tangent\:\frac{3}{(4x+1)^{2}}
derivative of (x^3/3+1)	\frac{d}{dx}(\frac{x^{3}}{3}+1)
area \sqrt[3]{x}, 1/x	area\:\sqrt[3]{x},\frac{1}{x}
limit as t approaches 0 of t/(t^2-t)	\lim\:_{t\to\:0}(\frac{t}{t^{2}-t})
derivative of x+1-e^x	\frac{d}{dx}(x+1-e^{x})
integral of 3sin(x)	\int\:3\sin(x)dx
derivative of 2x-x^2+2x^3	\frac{d}{dx}(2x-x^{2}+2x^{3})
derivative of x^3+3x^2-9x+7	\frac{d}{dx}(x^{3}+3x^{2}-9x+7)

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