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Popular Calculus Problems

limit as x approaches-3+of (x^3)/(x^2-9)	\lim\:_{x\to\:-3+}(\frac{x^{3}}{x^{2}-9})
derivative of y=tan(e^x)	derivative\:y=\tan(e^{x})
integral from 3 to 4 of x^2	\int\:_{3}^{4}x^{2}dx
derivative of (5x+1/(2sqrt(x)))	\frac{d}{dx}(\frac{5x+1}{2\sqrt{x}})
laplacetransform e^{3-t}	laplacetransform\:e^{3-t}
derivative of (-y^2/((x-y)^2))	\frac{d}{dx}(\frac{-y^{2}}{(x-y)^{2}})
(\partial ^2)/(\partial x^2)(sin^2(mx+ny))	\frac{\partial\:^{2}}{\partial\:x^{2}}(\sin^{2}(mx+ny))
inverse oflaplace 1/((s-1)^5)	inverselaplace\:\frac{1}{(s-1)^{5}}
derivative of 2x^3-5x	\frac{d}{dx}(2x^{3}-5x)
integral of 2/((x-2)^2)	\int\:\frac{2}{(x-2)^{2}}dx
area x=y^2-8,x=8	area\:x=y^{2}-8,x=8
integral of ((x+4)/(sqrt(x)))	\int\:(\frac{x+4}{\sqrt{x}})dx
(\partial)/(\partial x)(4x^{1/2}+y)	\frac{\partial\:}{\partial\:x}(4x^{\frac{1}{2}}+y)
integral of ((x^2-3x+2))/(x+1)	\int\:\frac{(x^{2}-3x+2)}{x+1}dx
integral from-infinity to 0 of 1/(3-7x)	\int\:_{-\infty\:}^{0}\frac{1}{3-7x}dx
integral of sin(2x)sin(x)	\int\:\sin(2x)\sin(x)dx
integral of sec(x)-tan(x)	\int\:\sec(x)-\tan(x)dx
inverse oflaplace (8.2)/(4.2x^2+4x+5)	inverselaplace\:\frac{8.2}{4.2x^{2}+4x+5}
inverse oflaplace (s^2)/((s^2-1)^2)	inverselaplace\:\frac{s^{2}}{(s^{2}-1)^{2}}
derivative of (10)/(x^2)	derivative\:\frac{10}{x^{2}}
sum from n=0 to infinity of 6/(n(n+3))	\sum\:_{n=0}^{\infty\:}\frac{6}{n(n+3)}
f(t)= 1/(t^2)	f(t)=\frac{1}{t^{2}}
tangent of f(x)= 1/(1+e^x),\at x=1	tangent\:f(x)=\frac{1}{1+e^{x}},\at\:x=1
integral of (6-2x)/(sqrt(8-4x-4x^2))	\int\:\frac{6-2x}{\sqrt{8-4x-4x^{2}}}dx
d/(d{z)}(sin({y}{z}))	\frac{d}{d{z}}(\sin({y}{z}))
integral of cot(x/2)	\int\:\cot(\frac{x}{2})dx
derivative of f(-2)=3x-7	derivative\:f(-2)=3x-7
derivative of f(x)=sin(pix)	derivative\:f(x)=\sin(πx)
d/(dy)(xsin(y)+ycos(x))	\frac{d}{dy}(x\sin(y)+y\cos(x))
integral from 0 to 1 of x^3	\int\:_{0}^{1}x^{3}dx
derivative of 3/(x(x^2-4))	\frac{d}{dx}(\frac{3}{x(x^{2}-4)})
slope of xy-2y^2=3	slope\:xy-2y^{2}=3
(\partial)/(\partial x)(6y^{x/z})	\frac{\partial\:}{\partial\:x}(6y^{\frac{x}{z}})
sec(x)dy=xcot(y)dx	\sec(x)dy=x\cot(y)dx
integral of ((x^2+1))/(e^x)	\int\:\frac{(x^{2}+1)}{e^{x}}dx
volumeabout y=0,y=sqrt(x),[0,1]	volumeabout\:y=0,y=\sqrt{x},[0,1]
derivative of f(x)= 5/(sqrt(x+4))	derivative\:f(x)=\frac{5}{\sqrt{x+4}}
integral from 0 to t of t^2e^{-t/4}	\int\:_{0}^{t}t^{2}e^{-\frac{t}{4}}dt
integral of (x+6)(3x-4)	\int\:(x+6)(3x-4)dx
integral from-2 to 0 of 3xsqrt(4-x^2)	\int\:_{-2}^{0}3x\sqrt{4-x^{2}}dx
(\partial)/(\partial x)(ln(2+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\ln(2+x^{2}+y^{2}))
(\partial)/(\partial y)(ln(y-3x))	\frac{\partial\:}{\partial\:y}(\ln(y-3x))
integral of-24te^{-3t}	\int\:-24te^{-3t}dt
(d^2)/(dx^2)(\sqrt[4]{x})	\frac{d^{2}}{dx^{2}}(\sqrt[4]{x})
integral of (x^2-x+2)/(x^4+4x^2+3)	\int\:\frac{x^{2}-x+2}{x^{4}+4x^{2}+3}dx
integral of in^2x	\int\:in^{2}xdx
tangent of y=sqrt(x^2-x+10),\at x=3	tangent\:y=\sqrt{x^{2}-x+10},\at\:x=3
derivative of cos(xln(cos(x))+xsin(x))	\frac{d}{dx}(\cos(x)\ln(\cos(x))+x\sin(x))
derivative of (ln(4x)/(4x))	\frac{d}{dx}(\frac{\ln(4x)}{4x})
area y=4-x^2,y=x+2	area\:y=4-x^{2},y=x+2
(\partial)/(\partial y)(1/(sqrt(xy)))	\frac{\partial\:}{\partial\:y}(\frac{1}{\sqrt{xy}})
integral of x/(sqrt(1+x^2))	\int\:\frac{x}{\sqrt{1+x^{2}}}dx
integral of 3/(x^2)-2/(x^3)	\int\:\frac{3}{x^{2}}-\frac{2}{x^{3}}dx
tangent of x^3	tangent\:x^{3}
derivative of ln(xe^x)	\frac{d}{dx}(\ln(x)e^{x})
derivative of (5x-4^2)	\frac{d}{dx}((5x-4)^{2})
derivative of f(x)=ln(1/x)	derivative\:f(x)=\ln(\frac{1}{x})
(dy)/(dt)=y-2t	\frac{dy}{dt}=y-2t
integral of x/(sqrt(x+8))	\int\:\frac{x}{\sqrt{x+8}}dx
limit as x approaches 2 of 1/(2-5x)	\lim\:_{x\to\:2}(\frac{1}{2-5x})
derivative of \sqrt[3]{(x+1/(x-1)})	\frac{d}{dx}(\sqrt[3]{\frac{x+1}{x-1}})
d/(dt)(e^{4t})	\frac{d}{dt}(e^{4t})
0.125y^{''}+4y^'+28y=0	0.125y^{\prime\:\prime\:}+4y^{\prime\:}+28y=0
derivative of 6x^3cos(x)	\frac{d}{dx}(6x^{3}\cos(x))
4xy^'+2y=10x^6	4xy^{\prime\:}+2y=10x^{6}
integral of (x^3+x^2)/(x^5)	\int\:\frac{x^{3}+x^{2}}{x^{5}}dx
derivative of (x^4-3x)^2	derivative\:(x^{4}-3x)^{2}
derivative of 13x	derivative\:13x
integral of (2x)/(e^{8x)}	\int\:\frac{2x}{e^{8x}}dx
slope of y=-3x^2-x	slope\:y=-3x^{2}-x
(d^2)/(dx^2)(1/(ln(x)))	\frac{d^{2}}{dx^{2}}(\frac{1}{\ln(x)})
d/(dy)(y^2)	\frac{d}{dy}(y^{2})
limit as x approaches infinity of 1/((2+x^2)^{1/x)}	\lim\:_{x\to\:\infty\:}(\frac{1}{(2+x^{2})^{\frac{1}{x}}})
f(x)=arctan(2x)	f(x)=\arctan(2x)
derivative of arccos(4x^3)	\frac{d}{dx}(\arccos(4x^{3}))
(d^2)/(dx^2)(x^2sin(sqrt(x)))	\frac{d^{2}}{dx^{2}}(x^{2}\sin(\sqrt{x}))
integral of 1/((x+y)^2)	\int\:\frac{1}{(x+y)^{2}}dx
sum from n=1 to infinity of (-1)^{n+1}	\sum\:_{n=1}^{\infty\:}(-1)^{n+1}
derivative of (t^4+t^5-1)/(t^6)	derivative\:\frac{t^{4}+t^{5}-1}{t^{6}}
integral of (4x+1)^6	\int\:(4x+1)^{6}dx
y^3-(18x+8)+3xy^2y^'=0	y^{3}-(18x+8)+3xy^{2}y^{\prime\:}=0
integral of 1/(y^3sqrt(y^2-9))	\int\:\frac{1}{y^{3}\sqrt{y^{2}-9}}dy
d/(dθ)(sin(4θ))	\frac{d}{dθ}(\sin(4θ))
integral of x(x^2-2)	\int\:x(x^{2}-2)dx
(f(t)\circ g(t))'	(f(t)\circ\:g(t))\prime\:
integral from 2 to 3 of (x+1)/(x^2-x)	\int\:_{2}^{3}\frac{x+1}{x^{2}-x}dx
limit as x approaches 1 of (3x+2)/(4x-5)	\lim\:_{x\to\:1}(\frac{3x+2}{4x-5})
(\partial)/(\partial x)(10-(3x^2+3y^2))	\frac{\partial\:}{\partial\:x}(10-(3x^{2}+3y^{2}))
derivative of 3x^2-4x+1	\frac{d}{dx}(3x^{2}-4x+1)
integral of 3/(e^{t/2)}	\int\:\frac{3}{e^{\frac{t}{2}}}dt
integral of e^{x^6}	\int\:e^{x^{6}}dx
integral of 6x^2sin(x^3)	\int\:6x^{2}\sin(x^{3})dx
integral of (12)/(x^2sqrt(x^2+16))	\int\:\frac{12}{x^{2}\sqrt{x^{2}+16}}dx
integral of 1/(9x^4)	\int\:\frac{1}{9x^{4}}dx
limit as x approaches 2-of 3	\lim\:_{x\to\:2-}(3)
integral of (z^2)/(1+z^3)	\int\:\frac{z^{2}}{1+z^{3}}dz
integral of x^2sqrt(x^2+4)	\int\:x^{2}\sqrt{x^{2}+4}dx
(\partial)/(\partial x)(2/x)	\frac{\partial\:}{\partial\:x}(\frac{2}{x})
integral of (x^4)/(sqrt(1-x^{10))}	\int\:\frac{x^{4}}{\sqrt{1-x^{10}}}dx
limit as x approaches infinity of ex	\lim\:_{x\to\:\infty\:}(ex)

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