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Popular Calculus Problems

integral of xsqrt(x^2-5)	\int\:x\sqrt{x^{2}-5}dx
limit as x approaches-1-of arccos(x)	\lim\:_{x\to\:-1-}(\arccos(x))
derivative of 32x	\frac{d}{dx}(32x)
limit as x approaches 0+of 10xln(x)	\lim\:_{x\to\:0+}(10x\ln(x))
limit as x approaches 2-of (-3)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{-3}{x^{2}-4})
laplacetransform 5e-3(t-2)	laplacetransform\:5e-3(t-2)
(\partial)/(\partial x)(3x^2y+2xy^2)	\frac{\partial\:}{\partial\:x}(3x^{2}y+2xy^{2})
limit as x approaches 3 of tan((3pi)/4)	\lim\:_{x\to\:3}(\tan(\frac{3π}{4}))
integral of 1/(2x+sqrt(x))	\int\:\frac{1}{2x+\sqrt{x}}dx
integral of re^{r/3}	\int\:re^{\frac{r}{3}}dr
(\partial)/(\partial x)(x^2+y^2-y^2x-2)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-y^{2}x-2)
limit as x approaches infinity+of x^3	\lim\:_{x\to\:\infty\:+}(x^{3})
limit as x approaches 0-of 18-4/(x^3)	\lim\:_{x\to\:0-}(18-\frac{4}{x^{3}})
derivative of e^{xsinh(x})	\frac{d}{dx}(e^{x\sinh(x)})
integral of x/(\sqrt[3]{x^2-8)}	\int\:\frac{x}{\sqrt[3]{x^{2}-8}}dx
integral of 4/(sqrt(x^2+16))	\int\:\frac{4}{\sqrt{x^{2}+16}}dx
derivative of f(v)=(v^{-3}+6v^{-2})^3	derivative\:f(v)=(v^{-3}+6v^{-2})^{3}
tangent of f(x)= 3/(x+1)	tangent\:f(x)=\frac{3}{x+1}
(\partial)/(\partial z)(xycos(x+yz))	\frac{\partial\:}{\partial\:z}(xy\cos(x+yz))
integral of (2-8x)/(sqrt(1-4x^2))	\int\:\frac{2-8x}{\sqrt{1-4x^{2}}}dx
limit as x approaches 1 of 3x^3+2x^2+4	\lim\:_{x\to\:1}(3x^{3}+2x^{2}+4)
integral of (x^5)/(sqrt(1-x^2))	\int\:\frac{x^{5}}{\sqrt{1-x^{2}}}dx
derivative of 4^{x+1}	derivative\:4^{x+1}
limit as x approaches 1 of 2x^3-4x^2+x+7	\lim\:_{x\to\:1}(2x^{3}-4x^{2}+x+7)
(\partial)/(\partial x)(cos(2y))	\frac{\partial\:}{\partial\:x}(\cos(2y))
integral of sqrt(39-10x-x^2)	\int\:\sqrt{39-10x-x^{2}}dx
derivative of sqrt(18x-x^2)	\frac{d}{dx}(\sqrt{18x-x^{2}})
derivative of 4x+8	\frac{d}{dx}(4x+8)
derivative of f(x)=x-1/x	derivative\:f(x)=x-\frac{1}{x}
integral from 0 to 1 of x^5ln(x)	\int\:_{0}^{1}x^{5}\ln(x)dx
derivative of 3arctan(2x)	\frac{d}{dx}(3\arctan(2x))
integral of ((z^4+10z^3)/(2z^2))	\int\:(\frac{z^{4}+10z^{3}}{2z^{2}})dz
y^'-(2y)/x =x^2e^x	y^{\prime\:}-\frac{2y}{x}=x^{2}e^{x}
(\partial)/(\partial x)(e^{-kx^2})	\frac{\partial\:}{\partial\:x}(e^{-kx^{2}})
(dy)/(dx)=y(x^2+2)	\frac{dy}{dx}=y(x^{2}+2)
derivative of 8e^{-7x}	derivative\:8e^{-7x}
y^'=x^3	y^{\prime\:}=x^{3}
integral from 7 to 9 of (x^2+2x-8)	\int\:_{7}^{9}(x^{2}+2x-8)dx
(\partial)/(\partial x)(sin(8θ))	\frac{\partial\:}{\partial\:x}(\sin(8θ))
integral of csc^2(y)	\int\:\csc^{2}(y)dy
(\partial)/(\partial x)(5x^{y/z})	\frac{\partial\:}{\partial\:x}(5x^{\frac{y}{z}})
xy^'=y+7x^2sin(x),y(pi)=0	xy^{\prime\:}=y+7x^{2}\sin(x),y(π)=0
limit as x approaches 1 of sqrt(5x+6)	\lim\:_{x\to\:1}(\sqrt{5x+6})
derivative of-3^{-2}(tan(7x)^5)	\frac{d}{dx}(-3^{-2}(\tan(7x))^{5})
(2cos(x))^'	(2\cos(x))^{\prime\:}
area y^2=x-2,y=x-4	area\:y^{2}=x-2,y=x-4
integral of (sec(2x)+tan(2x))	\int\:(\sec(2x)+\tan(2x))dx
derivative of f(x)=(2t+1)/(t+3)	derivative\:f(x)=\frac{2t+1}{t+3}
area y=2x^2+3,(0,3)	area\:y=2x^{2}+3,(0,3)
integral of (x^2+1)/(1-x^2)	\int\:\frac{x^{2}+1}{1-x^{2}}dx
limit as x approaches (5pi)/6 of sin(x)	\lim\:_{x\to\:\frac{5π}{6}}(\sin(x))
(dy)/(dx)=(xy)^2,y(0)=1	\frac{dy}{dx}=(xy)^{2},y(0)=1
integral of (x^5)/(x^6+2)	\int\:\frac{x^{5}}{x^{6}+2}dx
limit as x approaches 9 of 1/((x-9)^3)	\lim\:_{x\to\:9}(\frac{1}{(x-9)^{3}})
area 7cos(7x),7-7cos(7x)	area\:7\cos(7x),7-7\cos(7x)
integral of sec^9(x)tan(x)	\int\:\sec^{9}(x)\tan(x)dx
derivative of sin(pi*x)	\frac{d}{dx}(\sin(π\cdot\:x))
derivative of 7/(sqrt(x+8))	\frac{d}{dx}(\frac{7}{\sqrt{x+8}})
derivative of Ae^{-3x}	\frac{d}{dx}(Ae^{-3x})
integral of 1/(ln^2(x))	\int\:\frac{1}{\ln^{2}(x)}dx
area 2x^2+3,(-1,2)	area\:2x^{2}+3,(-1,2)
derivative of (1+cos^2(x)^6)	\frac{d}{dx}((1+\cos^{2}(x))^{6})
d/(dt)(15t^2)	\frac{d}{dt}(15t^{2})
-3y^'+(3y)/x =x^3y^4	-3y^{\prime\:}+\frac{3y}{x}=x^{3}y^{4}
(dy)/(dt)=2y+y^3,y(0)=1	\frac{dy}{dt}=2y+y^{3},y(0)=1
derivative of x^{2/7}	derivative\:x^{\frac{2}{7}}
derivative of 4x-3	derivative\:4x-3
tangent of y=(4x)/(1+x^2),(4, 16/17)	tangent\:y=\frac{4x}{1+x^{2}},(4,\frac{16}{17})
integral from 0 to pi/2 of-3sin^2(3x)	\int\:_{0}^{\frac{π}{2}}-3\sin^{2}(3x)dx
inverse oflaplace ((3-2s))/((s^2+4s+5))	inverselaplace\:\frac{(3-2s)}{(s^{2}+4s+5)}
integral of x^2-7x+5	\int\:x^{2}-7x+5dx
integral from 9/8 to 4 of 1/(1-x^2)	\int\:_{\frac{9}{8}}^{4}\frac{1}{1-x^{2}}dx
integral of-x/(1+x^2)	\int\:-\frac{x}{1+x^{2}}dx
derivative of e^{-1}	derivative\:e^{-1}
integral from 0 to 2 of e^{-x}+e	\int\:_{0}^{2}e^{-x}+edx
integral of te^{-6t}	\int\:te^{-6t}dt
derivative of (2x^2+6x+6/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+6x+6}{\sqrt{x}})
sum from n=1 to infinity of 4(0.8)^{n-1}	\sum\:_{n=1}^{\infty\:}4(0.8)^{n-1}
dx+e^{3x}dy=0	dx+e^{3x}dy=0
(d^2)/(dx^2)(-5/x)	\frac{d^{2}}{dx^{2}}(-\frac{5}{x})
derivative of (-10/(x^3))	\frac{d}{dx}(\frac{-10}{x^{3}})
e^xydy-(e^{-y}+e^{2x-y})dx=0	e^{x}ydy-(e^{-y}+e^{2x-y})dx=0
derivative of log_{e}(x^2+1)	\frac{d}{dx}(\log_{e}(x^{2}+1))
integral of (e^{3x})/(sqrt(1-e^{6x))}	\int\:\frac{e^{3x}}{\sqrt{1-e^{6x}}}dx
limit as x approaches infinity of (5-2x^{3/2})/(3x-4)	\lim\:_{x\to\:\infty\:}(\frac{5-2x^{\frac{3}{2}}}{3x-4})
integral of (1-x)(2+x^2)	\int\:(1-x)(2+x^{2})dx
derivative of arctan(7/(x^2))	derivative\:\arctan(\frac{7}{x^{2}})
derivative of (3sqrt(x)+4)x^2	derivative\:(3\sqrt{x}+4)x^{2}
integral of 7(sec(x))^2-4sin(x)	\int\:7(\sec(x))^{2}-4\sin(x)dx
integral of sqrt(x^2-3/4)	\int\:\sqrt{x^{2}-\frac{3}{4}}dx
derivative of sin(pi)	\frac{d}{dx}(\sin(π))
derivative of (x^3+2e^x)	\frac{d}{dx}((x^{3}+2)e^{x})
y^{''}-2y=5	y^{\prime\:\prime\:}-2y=5
integral of ((3inx-5)^4)/x	\int\:\frac{(3inx-5)^{4}}{x}dx
(dy)/(dx)=5y^2-y/x	\frac{dy}{dx}=5y^{2}-\frac{y}{x}
laplacetransform 6(t)e^{-2t}	laplacetransform\:6(t)e^{-2t}
(\partial)/(\partial x)((1+2xy^2)^3)	\frac{\partial\:}{\partial\:x}((1+2xy^{2})^{3})
derivative of y= t/((t-5)^2)	derivative\:y=\frac{t}{(t-5)^{2}}
integral of 5cos^3(6x)	\int\:5\cos^{3}(6x)dx
(\partial)/(\partial x)(3x^3+x^2y-3y^3)	\frac{\partial\:}{\partial\:x}(3x^{3}+x^{2}y-3y^{3})

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