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Popular Calculus Problems

(dx)/(dt)=x-2x^2	\frac{dx}{dt}=x-2x^{2}
area x^2,sqrt(x),[ 1/4 ,1]	area\:x^{2},\sqrt{x},[\frac{1}{4},1]
derivative of x^2arctan(3x)	\frac{d}{dx}(x^{2}\arctan(3x))
area y=1+2sqrt(x),y=((3+x))/3	area\:y=1+2\sqrt{x},y=\frac{(3+x)}{3}
derivative of (2x-3^4(x^2+x+1)^5)	\frac{d}{dx}((2x-3)^{4}(x^{2}+x+1)^{5})
y^{''}-4y=6e^{-x}	y^{\prime\:\prime\:}-4y=6e^{-x}
integral from 0 to 1 of x/(x^2+1)	\int\:_{0}^{1}\frac{x}{x^{2}+1}dx
y^4x^2y^'=1	y^{4}x^{2}y^{\prime\:}=1
inverse oflaplace 1/((x+4)^2)	inverselaplace\:\frac{1}{(x+4)^{2}}
tangent of 4e^xcos(x)	tangent\:4e^{x}\cos(x)
derivative of ln(2x)*4	derivative\:\ln(2x)\cdot\:4
derivative of 5^{-4x}	\frac{d}{dx}(5^{-4x})
limit as x approaches 0 of e^{5x}	\lim\:_{x\to\:0}(e^{5x})
area 4x+y^2=9,x=2y	area\:4x+y^{2}=9,x=2y
(\partial)/(\partial y)(e^xcos(y)+yz)	\frac{\partial\:}{\partial\:y}(e^{x}\cos(y)+yz)
derivative of 30sqrt(x)-3x	derivative\:30\sqrt{x}-3x
derivative of e^{-(x^2+y^2})	\frac{d}{dx}(e^{-(x^{2}+y^{2})})
tangent of ysin(8x)=xcos(2y),(pi/2 , pi/4)	tangent\:y\sin(8x)=x\cos(2y),(\frac{π}{2},\frac{π}{4})
derivative of 5sec(2x)	\frac{d}{dx}(5\sec(2x))
integral of yln(y)	\int\:y\ln(y)dy
implicit (dy)/(dx),e^{2x}sin(3x)-e^{-2x}sin(2y)=13xy^2	implicit\:\frac{dy}{dx},e^{2x}\sin(3x)-e^{-2x}\sin(2y)=13xy^{2}
derivative of cos(x)+sin(x)	derivative\:\cos(x)+\sin(x)
integral from 0 to k of 1/(x^2+1)	\int\:_{0}^{k}\frac{1}{x^{2}+1}dx
integral of (e^{2x})/2	\int\:\frac{e^{2x}}{2}dx
sum from n=0 to infinity of (n^3)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{n^{3}}{n!}
e^xy(dy)/(dx)=e^{-y}+e^{-7x-y}	e^{x}y\frac{dy}{dx}=e^{-y}+e^{-7x-y}
derivative of (-2x/((x^2-1)^2))	\frac{d}{dx}(\frac{-2x}{(x^{2}-1)^{2}})
integral of ((2x^3-x))/(x^4-x^2-25)	\int\:\frac{(2x^{3}-x)}{x^{4}-x^{2}-25}dx
derivative of (x^3/((x-2)^2))	\frac{d}{dx}(\frac{x^{3}}{(x-2)^{2}})
derivative of (tan(sqrt(x)-1)/(x^3+2))	\frac{d}{dx}(\frac{\tan(\sqrt{x}-1)}{x^{3}+2})
integral of 1/((2x+3y)^2)	\int\:\frac{1}{(2x+3y)^{2}}dx
integral of sin^2(3xco)s^23x	\int\:\sin^{2}(3xco)s^{2}3xdx
(dy)/(dx)=e^{y+x}	\frac{dy}{dx}=e^{y+x}
d/(dv)(usin(v))	\frac{d}{dv}(u\sin(v))
(\partial)/(\partial y)(ln(5+x^2y^2))	\frac{\partial\:}{\partial\:y}(\ln(5+x^{2}y^{2}))
tangent of f(x)=4x-x^2,\at x=2	tangent\:f(x)=4x-x^{2},\at\:x=2
slope of s=t^3-t^2	slope\:s=t^{3}-t^{2}
derivative of sqrt(16x-x^2)	\frac{d}{dx}(\sqrt{16x-x^{2}})
t^2y^{''}+7ty^'+9y=0	t^{2}y^{\prime\:\prime\:}+7ty^{\prime\:}+9y=0
integral of (x^5)/((x^3+1)^2)	\int\:\frac{x^{5}}{(x^{3}+1)^{2}}dx
limit as x approaches 1 of cos(pi/2 x)	\lim\:_{x\to\:1}(\cos(\frac{π}{2}x))
derivative of (x-5^{2/3})	\frac{d}{dx}((x-5)^{\frac{2}{3}})
derivative of arcsin(-3x)	\frac{d}{dx}(\arcsin(-3x))
y^{''}=-4y-4y^'	y^{\prime\:\prime\:}=-4y-4y^{\prime\:}
(\partial)/(\partial y)(tan(y))	\frac{\partial\:}{\partial\:y}(\tan(y))
tangent of log_{2}(x+x^{-2})	tangent\:\log_{2}(x+x^{-2})
limit as t approaches infinity of t^2	\lim\:_{t\to\:\infty\:}(t^{2})
limit as x approaches 2+of (e^{-x})/(2-x)	\lim\:_{x\to\:2+}(\frac{e^{-x}}{2-x})
integral of 2x(x^2+4)^7	\int\:2x(x^{2}+4)^{7}dx
integral from 0 to 2 of-x^3	\int\:_{0}^{2}-x^{3}dx
integral of (3x^3-2x^2)	\int\:(3x^{3}-2x^{2})dx
tangent of 3x^4+x^3-21x^2	tangent\:3x^{4}+x^{3}-21x^{2}
tangent of y=sqrt(x)(25.5)	tangent\:y=\sqrt{x}(25.5)
tangent of 7x^2	tangent\:7x^{2}
parity y=(arcsin(sec(x)))^{tanh(x)}	parity\:y=(\arcsin(\sec(x)))^{\tanh(x)}
derivative of f(x)= 6/(\sqrt[9]{x^7+5)}	derivative\:f(x)=\frac{6}{\sqrt[9]{x^{7}+5}}
integral of (ax+b)	\int\:(ax+b)dx
derivative of ln(arctan(cos(x)))	\frac{d}{dx}(\ln(\arctan(\cos(x))))
integral of cos(xpi)	\int\:\cos(xπ)dx
integral from 0 to 2pi of cos^2(t)	\int\:_{0}^{2π}\cos^{2}(t)dt
y=2^x+x^2(-1-x)^{sqrt(x)}	y=2^{x}+x^{2}(-1-x)^{\sqrt{x}}
integral of 2cos(x)e^x	\int\:2\cos(x)e^{x}dx
integral of 10e^{1-5x}	\int\:10e^{1-5x}dx
(\partial)/(\partial y)(3xsin(y))	\frac{\partial\:}{\partial\:y}(3x\sin(y))
integral of 7x^{2/5}+2x^{-4/5}	\int\:7x^{\frac{2}{5}}+2x^{-\frac{4}{5}}dx
derivative of tan(x^2+y)	\frac{d}{dx}(\tan(x^{2}+y))
derivative of 3arcsin(x)	\frac{d}{dx}(3\arcsin(x))
integral of 1/((x^2-81)^{3/2)}	\int\:\frac{1}{(x^{2}-81)^{\frac{3}{2}}}dx
inverse oflaplace 3/((s+2)^3)	inverselaplace\:\frac{3}{(s+2)^{3}}
area y=x^3-2x^2+2,y=3x^2+5x-23,-1,7	area\:y=x^{3}-2x^{2}+2,y=3x^{2}+5x-23,-1,7
(\partial)/(\partial x)(x^2e^{-x/y})	\frac{\partial\:}{\partial\:x}(x^{2}e^{-\frac{x}{y}})
integral from 1 to 5 of (e^{x/2})/(x^3)	\int\:_{1}^{5}\frac{e^{\frac{x}{2}}}{x^{3}}dx
area 3e^x,3xe^{x^2},[0,1]	area\:3e^{x},3xe^{x^{2}},[0,1]
limit as x approaches 6 of sqrt(2x-7)	\lim\:_{x\to\:6}(\sqrt{2x-7})
integral of ((x+6))/((x+1))	\int\:\frac{(x+6)}{(x+1)}dx
integral from 2 to 3 of (ln(2x^5))/(x^2)	\int\:_{2}^{3}\frac{\ln(2x^{5})}{x^{2}}dx
(\partial)/(\partial x)(x^ay^{1-a})	\frac{\partial\:}{\partial\:x}(x^{a}y^{1-a})
(\partial)/(\partial x)(sin(x+2y))	\frac{\partial\:}{\partial\:x}(\sin(x+2y))
integral from-1 to 1 of x(x^2+3)^3	\int\:_{-1}^{1}x(x^{2}+3)^{3}dx
limit as x approaches-2-of (3x-6)/(x+2)	\lim\:_{x\to\:-2-}(\frac{3x-6}{x+2})
derivative of pi/4 x	\frac{d}{dx}(\frac{π}{4}x)
integral of (sec(θ)tan(θ))/(1+sec(θ))	\int\:\frac{\sec(θ)\tan(θ)}{1+\sec(θ)}dθ
tangent of f(x)=-5x^2,\at x=2	tangent\:f(x)=-5x^{2},\at\:x=2
limit as x approaches 8 of x^3+1	\lim\:_{x\to\:8}(x^{3}+1)
integral from 3 to 5 of (y^2)/5+5/(4y^2)	\int\:_{3}^{5}\frac{y^{2}}{5}+\frac{5}{4y^{2}}dy
integral of sin(arccos(x))	\int\:\sin(\arccos(x))dx
integral of 3e^{-t}	\int\:3e^{-t}dt
5sqrt(xy)(dy)/(dx)=4	5\sqrt{xy}\frac{dy}{dx}=4
inverse oflaplace (e^{-s})/(s^2)	inverselaplace\:\frac{e^{-s}}{s^{2}}
integral of-x^2sin(x)	\int\:-x^{2}\sin(x)dx
(\partial)/(\partial x)((e^{7-x})/(y^5))	\frac{\partial\:}{\partial\:x}(\frac{e^{7-x}}{y^{5}})
(\partial)/(\partial x)(2y-xe^{xy})	\frac{\partial\:}{\partial\:x}(2y-xe^{xy})
sum from n=0 to infinity of 1/(n^{2/3)}	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{\frac{2}{3}}}
derivative of e^{(2x}(x^3+6x-1)ln(x))	\frac{d}{dx}(e^{(2x)}(x^{3}+6x-1)\ln(x))
derivative of (sin^2(x+1)/(cos^2(x)+1))	\frac{d}{dx}(\frac{\sin^{2}(x)+1}{\cos^{2}(x)+1})
derivative of x/8	derivative\:\frac{x}{8}
inverse oflaplace {((s-1))/(s+1)}	inverselaplace\:\left\{\frac{(s-1)}{s+1}\right\}
(\partial)/(\partial y)(e^{xy}+x^2z)	\frac{\partial\:}{\partial\:y}(e^{xy}+x^{2}z)
derivative of (x^4)/(1-x^3)	derivative\:\frac{x^{4}}{1-x^{3}}
area x^2,(-2,1)	area\:x^{2},(-2,1)

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