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Popular Calculus Problems

limit as x approaches 5 of 3x^2+3x+5	\lim\:_{x\to\:5}(3x^{2}+3x+5)
integral of 1/n	\int\:\frac{1}{n}dn
sum from n=1 to infinity of n/(e^n)	\sum\:_{n=1}^{\infty\:}\frac{n}{e^{n}}
integral of arctan(2x+1)	\int\:\arctan(2x+1)dx
integral of 3e^{4x}	\int\:3e^{4x}dx
integral of x^2-6	\int\:x^{2}-6dx
derivative of (x^2+1/(2x-3))	\frac{d}{dx}(\frac{x^{2}+1}{2x-3})
integral of (cos^2(x))/2	\int\:\frac{\cos^{2}(x)}{2}dx
derivative of sin^3(2t)	derivative\:\sin^{3}(2t)
limit as x approaches 2 of ((x^2-5x+4))/(x-2)	\lim\:_{x\to\:2}(\frac{(x^{2}-5x+4)}{x-2})
integral from 0 to 2 of (2x)/((x^2+1)^2)	\int\:_{0}^{2}\frac{2x}{(x^{2}+1)^{2}}dx
(\partial)/(\partial x)(4e^{5x})	\frac{\partial\:}{\partial\:x}(4e^{5x})
derivative of 4x+6	derivative\:4x+6
integral of x^4-x	\int\:x^{4}-xdx
-y^{''}+y^'+y=0	-y^{\prime\:\prime\:}+y^{\prime\:}+y=0
derivative of (x^2-3x+2/(2x^2+5x-1))	\frac{d}{dx}(\frac{x^{2}-3x+2}{2x^{2}+5x-1})
(\partial)/(\partial y)((2y)/(x+y^2))	\frac{\partial\:}{\partial\:y}(\frac{2y}{x+y^{2}})
integral of (5sqrt(ln^2(x)+9))/x	\int\:\frac{5\sqrt{\ln^{2}(x)+9}}{x}dx
(\partial)/(\partial x)(y^2+xy+3y+2x+3)	\frac{\partial\:}{\partial\:x}(y^{2}+xy+3y+2x+3)
integral of 1/(5sin(x)+3)	\int\:\frac{1}{5\sin(x)+3}dx
(\partial)/(\partial x)(x^2+y^2+3xy+15x)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+3xy+15x)
(\partial)/(\partial t)(e^{-t}sin(t))	\frac{\partial\:}{\partial\:t}(e^{-t}\sin(t))
integral of (a^{5x}+e^{5x})	\int\:(a^{5x}+e^{5x})dx
integral of 1/(4-y^2)	\int\:\frac{1}{4-y^{2}}dy
integral of sin^8(3x)cos^5(3x)	\int\:\sin^{8}(3x)\cos^{5}(3x)dx
derivative of f(x)=ln(x^2-8x+16)	derivative\:f(x)=\ln(x^{2}-8x+16)
(\partial)/(\partial x)(cos^2(θ))	\frac{\partial\:}{\partial\:x}(\cos^{2}(θ))
derivative of x^{(2/3})	\frac{d}{dx}(x^{(\frac{2}{3})})
(dy)/(dx)=6xe^y	\frac{dy}{dx}=6xe^{y}
derivative of C(x)=-9x^2+500x+110	derivative\:C(x)=-9x^{2}+500x+110
derivative of ((x-1^4)/((x^2+2x)^5))	\frac{d}{dx}(\frac{(x-1)^{4}}{(x^{2}+2x)^{5}})
d/(dy)(e^x(x-y)^2)	\frac{d}{dy}(e^{x}(x-y)^{2})
(\partial)/(\partial x)(cos^3(x))	\frac{\partial\:}{\partial\:x}(\cos^{3}(x))
(\partial)/(\partial y)((4sqrt(x))/(3y^2+1))	\frac{\partial\:}{\partial\:y}(\frac{4\sqrt{x}}{3y^{2}+1})
limit as x approaches 2 of 3+x	\lim\:_{x\to\:2}(3+x)
derivative of (e^x/(7x^2))	\frac{d}{dx}(\frac{e^{x}}{7x^{2}})
area sin(x),5x, pi/2 ,pi	area\:\sin(x),5x,\frac{π}{2},π
limit as x approaches-2 of x+3	\lim\:_{x\to\:-2}(x+3)
derivative of f(x)=(x^2-5)e^x	derivative\:f(x)=(x^{2}-5)e^{x}
(\partial)/(\partial y)(1)	\frac{\partial\:}{\partial\:y}(1)
(dx)/(dt)=5x(8-x)	\frac{dx}{dt}=5x(8-x)
derivative of sin(5xln(sin^2(5x)))	\frac{d}{dx}(\sin(5x)\ln(\sin^{2}(5x)))
inverse oflaplace (10)/(s^3+2s^2+20s)	inverselaplace\:\frac{10}{s^{3}+2s^{2}+20s}
integral from 0 to 1 of 0	\int\:_{0}^{1}0dx
integral from 0 to 1 of 1/(4y-1)	\int\:_{0}^{1}\frac{1}{4y-1}dy
derivative of f(x)= 6/x	derivative\:f(x)=\frac{6}{x}
limit as x approaches 0 of ((2x^2+16))/x	\lim\:_{x\to\:0}(\frac{(2x^{2}+16)}{x})
taylor x^2e^{x^2}	taylor\:x^{2}e^{x^{2}}
sum from n=1 to infinity of n*(3/4)^n	\sum\:_{n=1}^{\infty\:}n\cdot\:(\frac{3}{4})^{n}
integral of (sqrt(9-x^2))/(x^3)	\int\:\frac{\sqrt{9-x^{2}}}{x^{3}}dx
integral of 1/(x^2sqrt(16-x^2))	\int\:\frac{1}{x^{2}\sqrt{16-x^{2}}}dx
derivative of \sqrt[5]{x^2-x+7}	\frac{d}{dx}(\sqrt[5]{x^{2}-x+7})
(\partial)/(\partial z)(2y^3z)	\frac{\partial\:}{\partial\:z}(2y^{3}z)
derivative of sqrt(x^2+x+1)	\frac{d}{dx}(\sqrt{x^{2}+x+1})
(\partial)/(\partial y)(x^2-xy+y^2-y)	\frac{\partial\:}{\partial\:y}(x^{2}-xy+y^{2}-y)
integral of x^5(cos(x^3))	\int\:x^{5}(\cos(x^{3}))dx
d/(dz)(ln(sqrt((a^2-z^2)/(a^2+z^2))))	\frac{d}{dz}(\ln(\sqrt{\frac{a^{2}-z^{2}}{a^{2}+z^{2}}}))
derivative of 1/3 pi{r}(x(x)^2h)	\frac{d}{dx}(\frac{1}{3}π{r}(x)(x)^{2}h)
integral from 0 to 7 of 1/(sqrt(9+x^2))	\int\:_{0}^{7}\frac{1}{\sqrt{9+x^{2}}}dx
derivative of x^2-y	\frac{d}{dx}(x^{2}-y)
integral of (x^2)/(sqrt((x^2+6)))	\int\:\frac{x^{2}}{\sqrt{(x^{2}+6)}}dx
derivative of (3x^2-3x+1)(x^3)	derivative\:(3x^{2}-3x+1)(x^{3})
integral of 1/((4+x^2)^{5/2)}	\int\:\frac{1}{(4+x^{2})^{\frac{5}{2}}}dx
integral of ((5+ln(x))^5)/x	\int\:\frac{(5+\ln(x))^{5}}{x}dx
derivative of f(x)=6cos^4(3x+2)	derivative\:f(x)=6\cos^{4}(3x+2)
limit as x approaches 5 of x^3-x^2+5x	\lim\:_{x\to\:5}(x^{3}-x^{2}+5x)
y^'=ytan(t)+sin(t)	y^{\prime\:}=y\tan(t)+\sin(t)
limit as x approaches 1 of x^5-2x-6	\lim\:_{x\to\:1}(x^{5}-2x-6)
derivative of (csc(x)/(1+csc(x)))	\frac{d}{dx}(\frac{\csc(x)}{1+\csc(x)})
y^{''}+4y=e^{4x}	y^{\prime\:\prime\:}+4y=e^{4x}
integral of e^{e^x}	\int\:e^{e^{x}}dx
derivative of (2x-1/(x-1))	\frac{d}{dx}(\frac{2x-1}{x-1})
(\partial)/(\partial x)(-xe^{-xy})	\frac{\partial\:}{\partial\:x}(-xe^{-xy})
laplacetransform-1	laplacetransform\:-1
(\partial)/(\partial y)(xe^xsin(y))	\frac{\partial\:}{\partial\:y}(xe^{x}\sin(y))
tangent of (3x^4-12)^{1/2}	tangent\:(3x^{4}-12)^{\frac{1}{2}}
integral of xcos(3pi)x^2	\int\:x\cos(3π)x^{2}dx
(\partial)/(\partial y)(6x^2)	\frac{\partial\:}{\partial\:y}(6x^{2})
integral of (6+x^2)/x	\int\:\frac{6+x^{2}}{x}dx
derivative of (x+1)(7sqrt(x)+2)	derivative\:(x+1)(7\sqrt{x}+2)
(\partial)/(\partial x)(x/(y^2)+xy+8)	\frac{\partial\:}{\partial\:x}(\frac{x}{y^{2}}+xy+8)
derivative of ln(((2x+1^3)/((3x-1)^4)))	\frac{d}{dx}(\ln(\frac{(2x+1)^{3}}{(3x-1)^{4}}))
taylor z(z+1)e^z	taylor\:z(z+1)e^{z}
(\partial)/(\partial x)((2xy-1)e^{-xy})	\frac{\partial\:}{\partial\:x}((2xy-1)e^{-xy})
derivative of e^{2(x-1^2}+x/(1+x^3))	\frac{d}{dx}(e^{2(x-1)^{2}}+\frac{x}{1+x^{3}})
tangent of y=8x+12-15e^x,(0,-3)	tangent\:y=8x+12-15e^{x},(0,-3)
integral of (3+x)/(1+x^2)	\int\:\frac{3+x}{1+x^{2}}dx
area x^2+10,9x,0	area\:x^{2}+10,9x,0
integral of ((9-y^2)^2)/2-y(9-y^2)	\int\:\frac{(9-y^{2})^{2}}{2}-y(9-y^{2})dy
integral of sqrt(y+4)	\int\:\sqrt{y+4}dy
derivative of (2x/(x^4+1))	\frac{d}{dx}(\frac{2x}{x^{4}+1})
integral from 1 to 4 of-10sqrt(t)ln(t)	\int\:_{1}^{4}-10\sqrt{t}\ln(t)dt
integral of 10x^5e^{-x^3}	\int\:10x^{5}e^{-x^{3}}dx
derivative of-3x^2+2	\frac{d}{dx}(-3x^{2}+2)
roots Ax+B	roots\:Ax+B
inverse oflaplace e^{-,\at}	inverselaplace\:e^{-,\at\:}
integral of 4/(3-e^x)	\int\:\frac{4}{3-e^{x}}dx
area x^2+2x+11,-4x+2,[0]	area\:x^{2}+2x+11,-4x+2,[0]
integral of 3/(1-x^2)	\int\:\frac{3}{1-x^{2}}dx
(\partial)/(\partial x)(x^4+y^4-4x^2y^2)	\frac{\partial\:}{\partial\:x}(x^{4}+y^{4}-4x^{2}y^{2})

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