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Popular Calculus Problems

integral from 1 to 5 of sqrt(37)	\int\:_{1}^{5}\sqrt{37}dx
integral from-infinity to 0 of x5^{-x^2}	\int\:_{-\infty\:}^{0}x5^{-x^{2}}dx
integral of sqrt(16+y^2)	\int\:\sqrt{16+y^{2}}dy
(\partial)/(\partial x)(54x^8y^5-40x^7y^4)	\frac{\partial\:}{\partial\:x}(54x^{8}y^{5}-40x^{7}y^{4})
integral of (ln(x))/x	\int\:\frac{\ln(x)}{x}dx
derivative of f(x)=(3)e-5x	derivative\:f(x)=(3)e-5x
derivative of (x^2+4^2)	\frac{d}{dx}((x^{2}+4)^{2})
derivative of xe^x+e^x	derivative\:xe^{x}+e^{x}
(dy)/(dx)=(-x^2y)/(1+x^3)	\frac{dy}{dx}=\frac{-x^{2}y}{1+x^{3}}
d/(dt)(1+(t-y)^2)	\frac{d}{dt}(1+(t-y)^{2})
derivative of 1/((3+x^3))	\frac{d}{dx}(\frac{1}{(3+x)^{3}})
limit as x approaches 6 of (x^2-3)/(x-6)	\lim\:_{x\to\:6}(\frac{x^{2}-3}{x-6})
limit as x approaches-2 of sqrt(2x)	\lim\:_{x\to\:-2}(\sqrt{2x})
(\partial)/(\partial x)(2/(x-3))	\frac{\partial\:}{\partial\:x}(\frac{2}{x-3})
derivative of 2arcsin(x^4)	derivative\:2\arcsin(x^{4})
limit as x approaches infinity of 6(1+1/x)^{x^2}	\lim\:_{x\to\:\infty\:}(6(1+\frac{1}{x})^{x^{2}})
derivative of (5x^4)/(e^x)	derivative\:\frac{5x^{4}}{e^{x}}
(\partial)/(\partial y)(x-sqrt(y^2+z^2))	\frac{\partial\:}{\partial\:y}(x-\sqrt{y^{2}+z^{2}})
integral from 2 to 4 of sqrt(16-x^2)	\int\:_{2}^{4}\sqrt{16-x^{2}}dx
derivative of 6e^{2t}	derivative\:6e^{2t}
derivative of sin^2(cos(x))	\frac{d}{dx}(\sin^{2}(\cos(x)))
(\partial)/(\partial y)(6y)	\frac{\partial\:}{\partial\:y}(6y)
integral of z/(z+1)	\int\:\frac{z}{z+1}dz
derivative of 12(2x-3)^5	derivative\:12(2x-3)^{5}
integral of 1-cos(t)	\int\:1-\cos(t)dt
4x^2y^'=y^'+4xe^{-y}	4x^{2}y^{\prime\:}=y^{\prime\:}+4xe^{-y}
2sec(2t)2t*y^'=1	2\sec(2t)2t\cdot\:y^{\prime\:}=1
area y=3x^3,y=75x	area\:y=3x^{3},y=75x
derivative of sqrt(x-3)	derivative\:\sqrt{x-3}
derivative of 7pir^2	derivative\:7πr^{2}
tangent of x^2-7	tangent\:x^{2}-7
(y^')/(sqrt(y))=6x^2	\frac{y^{\prime\:}}{\sqrt{y}}=6x^{2}
implicit (dy)/(dx),y*cos(x)=2x^2+5y^2	implicit\:\frac{dy}{dx},y\cdot\:\cos(x)=2x^{2}+5y^{2}
integral from 5 to 8 of x/(x^2+6x+13)	\int\:_{5}^{8}\frac{x}{x^{2}+6x+13}dx
integral from 1/7 to 5 of 14xln(7x)	\int\:_{\frac{1}{7}}^{5}14x\ln(7x)dx
f(x)=(x+1)(x^3+x-2)	f(x)=(x+1)(x^{3}+x-2)
integral from 1 to 4 of (x^2+6)/(5x-x^2)	\int\:_{1}^{4}\frac{x^{2}+6}{5x-x^{2}}dx
integral of cos^2(pi)x	\int\:\cos^{2}(π)xdx
derivative of x^3+x^2+x+5	\frac{d}{dx}(x^{3}+x^{2}+x+5)
integral of sqrt(x^7)sin(1+x^{9/2})	\int\:\sqrt{x^{7}}\sin(1+x^{\frac{9}{2}})dx
limit as x approaches 3 of 7/((x-3)^2)	\lim\:_{x\to\:3}(\frac{7}{(x-3)^{2}})
tangent of f(x)=(x^2)/(x+6)	tangent\:f(x)=\frac{x^{2}}{x+6}
limit as x approaches-infinity of 2^x+3	\lim\:_{x\to\:-\infty\:}(2^{x}+3)
y^{''}-y^'+1/4 y=5+e^{x/2}	y^{\prime\:\prime\:}-y^{\prime\:}+\frac{1}{4}y=5+e^{\frac{x}{2}}
derivative of x^2(1-8x)	derivative\:x^{2}(1-8x)
(dN)/(dt)+N=Nte^{t+8}	\frac{dN}{dt}+N=Nte^{t+8}
derivative of (1+x^3/(1-x^3))	\frac{d}{dx}(\frac{1+x^{3}}{1-x^{3}})
integral of 1+2sin(θ)+sin^2(θ)	\int\:1+2\sin(θ)+\sin^{2}(θ)dθ
taylor sin(3x)	taylor\:\sin(3x)
integral of 4e^{cos(x)}sin(x)	\int\:4e^{\cos(x)}\sin(x)dx
integral of (2sin(x))/(cos(x))	\int\:\frac{2\sin(x)}{\cos(x)}dx
f(x)=tan(8x)	f(x)=\tan(8x)
integral of 1/((x^2+4)(x+2))	\int\:\frac{1}{(x^{2}+4)(x+2)}dx
limit as t approaches 0 of tan(7t)	\lim\:_{t\to\:0}(\tan(7t))
(\partial)/(\partial x)(10x^5y^4e^{-x})	\frac{\partial\:}{\partial\:x}(10x^{5}y^{4}e^{-x})
derivative of e^{log_{3}(x})	\frac{d}{dx}(e^{\log_{3}(x)})
(\partial)/(\partial x)(r^2cos^2(x))	\frac{\partial\:}{\partial\:x}(r^{2}\cos^{2}(x))
integral from-6 to 6 of (6-\|x\|)	\int\:_{-6}^{6}(6-\left\|x\right\|)dx
f(x)=sqrt(tan(x^2))	f(x)=\sqrt{\tan(x^{2})}
derivative of (2x-1^2ln(3x+4))	\frac{d}{dx}((2x-1)^{2}\ln(3x+4))
integral of 20e^{5x}	\int\:20e^{5x}dx
integral of nx	\int\:nxdx
derivative of 2/((1-2x^2))	\frac{d}{dx}(\frac{2}{(1-2x)^{2}})
integral of (2x^4+1)/(5x^3)	\int\:\frac{2x^{4}+1}{5x^{3}}dx
derivative of (xsinh(x+cos(x))^5)	\frac{d}{dx}((x\sinh(x)+\cos(x))^{5})
integral of xsin(1/10)x	\int\:x\sin(\frac{1}{10})xdx
integral from 0 to 1 of 2pi(x+9)x^2	\int\:_{0}^{1}2π(x+9)x^{2}dx
(1+y)dx-(1-x)dy=0	(1+y)dx-(1-x)dy=0
limit as x approaches 10 of x/2	\lim\:_{x\to\:10}(\frac{x}{2})
derivative of y=e^{7x+1}	derivative\:y=e^{7x+1}
integral of x^2*(1+2x^3)^5	\int\:x^{2}\cdot\:(1+2x^{3})^{5}dx
derivative of 9sqrt(x)-1/x	\frac{d}{dx}(9\sqrt{x}-\frac{1}{x})
derivative of f(x)=4x^5ln(x)	derivative\:f(x)=4x^{5}\ln(x)
laplacetransform e^{20t}	laplacetransform\:e^{20t}
y^'=((xy^2))/((1+x^2))	y^{\prime\:}=\frac{(xy^{2})}{(1+x^{2})}
y^{''}-16y^'+64y=0,y(0)=1,y(1)=0	y^{\prime\:\prime\:}-16y^{\prime\:}+64y=0,y(0)=1,y(1)=0
limit as x approaches 0 of (1-2x)^{3/x}	\lim\:_{x\to\:0}((1-2x)^{\frac{3}{x}})
derivative of ln(361sin^2(x))	derivative\:\ln(361\sin^{2}(x))
(\partial)/(\partial y)(sin(-2x)cos(8y))	\frac{\partial\:}{\partial\:y}(\sin(-2x)\cos(8y))
(x+y)dx+xdy=0	(x+y)dx+xdy=0
integral of 1/5 cos(5x)	\int\:\frac{1}{5}\cos(5x)dx
limit as x approaches infinity of coth(x)	\lim\:_{x\to\:\infty\:}(\coth(x))
integral of (2x+1)y^2sin(2xy)	\int\:(2x+1)y^{2}\sin(2xy)dx
(\partial)/(\partial x)(xysin(x)+ye^{xy})	\frac{\partial\:}{\partial\:x}(xy\sin(x)+ye^{xy})
derivative of f(x)=(5x-7)/(6x-9)	derivative\:f(x)=\frac{5x-7}{6x-9}
integral of e^xsqrt(29+e^x)	\int\:e^{x}\sqrt{29+e^{x}}dx
integral of xe^{tx}	\int\:xe^{tx}dx
(dy)/(dt)=7te^{-y},y(0)=3	\frac{dy}{dt}=7te^{-y},y(0)=3
d/(dy)(7y)	\frac{d}{dy}(7y)
integral of ((ln(x))^8)/x	\int\:\frac{(\ln(x))^{8}}{x}dx
integral of (x^2+x+1)sin(x)	\int\:(x^{2}+x+1)\sin(x)dx
limit as x approaches-1 of 1+x	\lim\:_{x\to\:-1}(1+x)
derivative of (-12x/((x^2+3)^2))	\frac{d}{dx}(\frac{-12x}{(x^{2}+3)^{2}})
derivative of 2x^2-6x+3	derivative\:2x^{2}-6x+3
(\partial)/(\partial x)(arccos(xy))	\frac{\partial\:}{\partial\:x}(\arccos(xy))
integral of e^{-3x}tan(e^{-3x})	\int\:e^{-3x}\tan(e^{-3x})dx
integral from 2 to 3 of (27)/(sqrt(3-x))	\int\:_{2}^{3}\frac{27}{\sqrt{3-x}}dx
integral of (5e^x)/(e^x+4)	\int\:\frac{5e^{x}}{e^{x}+4}dx
limit as x approaches 8-of (6x)/(x-8)	\lim\:_{x\to\:8-}(\frac{6x}{x-8})
f(t)=t^2+1	f(t)=t^{2}+1

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