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Popular Calculus Problems

integral of xsqrt(1+3x)	\int\:x\sqrt{1+3x}dx
(\partial)/(\partial x)(x-2y^2-2z^2)	\frac{\partial\:}{\partial\:x}(x-2y^{2}-2z^{2})
integral from 1 to 9 of (x-1)/(sqrt(x))	\int\:_{1}^{9}\frac{x-1}{\sqrt{x}}dx
limit as x approaches 2 of 3x^2-4x+2	\lim\:_{x\to\:2}(3x^{2}-4x+2)
derivative of x^3(x-3)^2	derivative\:x^{3}(x-3)^{2}
derivative of x/(x^3-1)	\frac{d}{dx}(\frac{x}{x^{3}-1})
integral of (u+4)(2u+1)	\int\:(u+4)(2u+1)du
y^{''}-2y^'+2y=cos(t),y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}-2y^{\prime\:}+2y=\cos(t),y(0)=1,y^{\prime\:}(0)=0
integral of 1/(sqrt(2+x^2))	\int\:\frac{1}{\sqrt{2+x^{2}}}dx
integral of 1/(x^2)e^{ln(x)}	\int\:\frac{1}{x^{2}}e^{\ln(x)}dx
derivative of (2x^3/3-8x-5)	\frac{d}{dx}(\frac{2x^{3}}{3}-8x-5)
area y=tan(7x),y=2sin(7x)	area\:y=\tan(7x),y=2\sin(7x)
x(dy)/(dx)+y=y^2	x\frac{dy}{dx}+y=y^{2}
derivative of x^2+x	derivative\:x^{2}+x
integral from-2 to 2 of (x^3)	\int\:_{-2}^{2}(x^{3})dx
derivative of (54/x)	\frac{d}{dx}(\frac{54}{x})
integral of (2x-5)/(x^3+4x^2+4x)	\int\:\frac{2x-5}{x^{3}+4x^{2}+4x}dx
integral of 1/(1/x+2)	\int\:\frac{1}{\frac{1}{x}+2}dx
limit as x approaches 0 of 5x-6	\lim\:_{x\to\:0}(5x-6)
area 2y=4sqrt(x),y=4,2y+4x=8	area\:2y=4\sqrt{x},y=4,2y+4x=8
integral of 1 x^2	\int\:\frac{d}{1}x^{2}dx
tangent of sin(3x)+cos(8x)	tangent\:\sin(3x)+\cos(8x)
simplify 1/3 x^6(x^2-3)	simplify\:\frac{1}{3}x^{6}(x^{2}-3)
derivative of (5-2x^{-2})	\frac{d}{dx}((5-2x)^{-2})
derivative of 1+12sqrt(t)	derivative\:1+12\sqrt{t}
y^{''}+9y=sin(3t)	y^{\prime\:\prime\:}+9y=\sin(3t)
derivative of \sqrt[8]{8x^7-10}	\frac{d}{dx}(\sqrt[8]{8x^{7}-10})
(dy)/(dx)=arctan(-6x)	\frac{dy}{dx}=\arctan(-6x)
y=((2x+1)/(3x-1))^4	y=(\frac{2x+1}{3x-1})^{4}
integral of e^{-6x}	\int\:e^{-6x}dx
sum from n=1 to infinity of (x-3)^n	\sum\:_{n=1}^{\infty\:}(x-3)^{n}
limit as x approaches 1 of 4/(x-1)	\lim\:_{x\to\:1}(\frac{4}{x-1})
(d^2)/(dx^2)(2x^3)	\frac{d^{2}}{dx^{2}}(2x^{3})
(dy)/(dx)-2y=1-2x	\frac{dy}{dx}-2y=1-2x
limit as a approaches-2 of a^2+3m-1	\lim\:_{a\to\:-2}(a^{2}+3m-1)
y^{''}+y^'+y=5cos(4x)	y^{\prime\:\prime\:}+y^{\prime\:}+y=5\cos(4x)
tangent of f(x)=x^2+3x+4pi	tangent\:f(x)=x^{2}+3x+4π
limit as t approaches 0 of 2e^{-t}	\lim\:_{t\to\:0}(2e^{-t})
limit as x approaches 0 of (8x^2-2x)/(2x)	\lim\:_{x\to\:0}(\frac{8x^{2}-2x}{2x})
integral of (2x-sqrt(x))^2	\int\:(2x-\sqrt{x})^{2}dx
(\partial)/(\partial x)(4sin(x)cos(y))	\frac{\partial\:}{\partial\:x}(4\sin(x)\cos(y))
(\partial}{\partial {K}}(L^{1/2)/K ^{1/2})	\frac{\partial\:}{\partial\:{K}}(L^{\frac{1}{2}}{K}^{\frac{1}{2}})
limit as x approaches 4 of x+4	\lim\:_{x\to\:4}(x+4)
derivative of f(x)=4x-7	derivative\:f(x)=4x-7
integral from 0 to 4 of sqrt(y)	\int\:_{0}^{4}\sqrt{y}dy
derivative of (2x+5^4)	\frac{d}{dx}((2x+5)^{4})
inverse oflaplace 5/(s^2+2s+5)	inverselaplace\:\frac{5}{s^{2}+2s+5}
derivative of ln(1+4x^2)	\frac{d}{dx}(\ln(1+4x^{2}))
integral from-1 to 3 of-x^2	\int\:_{-1}^{3}-x^{2}dx
derivative of 6/(5x^3)	\frac{d}{dx}(\frac{6}{5x^{3}})
integral of sin^2(x/2)cos(x/2)	\int\:\sin^{2}(\frac{x}{2})\cos(\frac{x}{2})dx
derivative of f(x)=(6x+5)(x^3-2)	derivative\:f(x)=(6x+5)(x^{3}-2)
limit as x approaches+3 of 0	\lim\:_{x\to\:+3}(0)
derivative of-y/(x+5e)	derivative\:-\frac{y}{x+5e}
integral of cos^4(x)sin^3(x)	\int\:\cos^{4}(x)\sin^{3}(x)dx
derivative of sin(6x)	derivative\:\sin(6x)
limit as x approaches 0 of x^3sin(x)	\lim\:_{x\to\:0}(x^{3}\sin(x))
limit as x approaches-infinity of 1-e^{-x}-xe^{-x}	\lim\:_{x\to\:-\infty\:}(1-e^{-x}-xe^{-x})
derivative of f(x)=x^4-12x^3+3	derivative\:f(x)=x^{4}-12x^{3}+3
integral of 8sin^3(x)cos(x)	\int\:8\sin^{3}(x)\cos(x)dx
(\partial)/(\partial x)(xyln(xy))	\frac{\partial\:}{\partial\:x}(xy\ln(xy))
tangent of f(x)=\sqrt[3]{x},\at x=64	tangent\:f(x)=\sqrt[3]{x},\at\:x=64
integral of 2x^2+5	\int\:2x^{2}+5dx
(xdy)/(dx)=-y+2x^2y,y(1)=1	\frac{xdy}{dx}=-y+2x^{2}y,y(1)=1
derivative of 9x-8sqrt(x)	\frac{d}{dx}(9x-8\sqrt{x})
limit as y approaches 2 of sqrt(4y^2-2y)	\lim\:_{y\to\:2}(\sqrt{4y^{2}-2y})
integral from 0 to-0.3 of 300x	\int\:_{0}^{-0.3}300xdx
integral of 3t^{-4}	\int\:3t^{-4}dt
integral of 1/((x+2)^2(x-5))	\int\:\frac{1}{(x+2)^{2}(x-5)}dx
integral of sin(3θ)	\int\:\sin(3θ)dθ
tangent of f(x)=e^{2x},\at x= 1/2 ln(3)	tangent\:f(x)=e^{2x},\at\:x=\frac{1}{2}\ln(3)
derivative of ((t^3)/(t^6+7))^2	derivative\:(\frac{t^{3}}{t^{6}+7})^{2}
integral of x/(sqrt(16+x^2))	\int\:\frac{x}{\sqrt{16+x^{2}}}dx
limit as x approaches 3 of 2x+\|x-3\|	\lim\:_{x\to\:3}(2x+\left\|x-3\right\|)
limit as x approaches 7 of (x+5)/(x+9)	\lim\:_{x\to\:7}(\frac{x+5}{x+9})
x^2y^{''}+xy^'+9y=10x	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}+9y=10x
slope of y=x^3+2	slope\:y=x^{3}+2
integral of tan^3(6x)	\int\:\tan^{3}(6x)dx
integral of x/(sqrt(x^2-6x+5))	\int\:\frac{x}{\sqrt{x^{2}-6x+5}}dx
integral of (7+x-3x^2)e^{-x}	\int\:(7+x-3x^{2})e^{-x}dx
derivative of sqrt(sin(x))	derivative\:\sqrt{\sin(x)}
tangent of 2x^3+3x^2-12x+8	tangent\:2x^{3}+3x^{2}-12x+8
limit as x approaches infinity of e^{nx}	\lim\:_{x\to\:\infty\:}(e^{nx})
derivative of (2x/(\sqrt[3]{x-2)})	\frac{d}{dx}(\frac{2x}{\sqrt[3]{x-2}})
integral of x(x+1)	\int\:x(x+1)dx
implicit (dy)/(dx),e^{x/y}=x-y	implicit\:\frac{dy}{dx},e^{\frac{x}{y}}=x-y
y^{''}+16.67y^'+10000y=0	y^{\prime\:\prime\:}+16.67y^{\prime\:}+10000y=0
tangent of y=6x^2-6x+3,(1,3)	tangent\:y=6x^{2}-6x+3,(1,3)
integral of 9y	\int\:9ydy
integral of 2/3 x^{-1/3}	\int\:\frac{2}{3}x^{-\frac{1}{3}}dx
limit as n approaches 0 of (1+n)^{1/n}	\lim\:_{n\to\:0}((1+n)^{\frac{1}{n}})
derivative of f(x)= 7/(x^3)	derivative\:f(x)=\frac{7}{x^{3}}
volumeabout y=0,y=ln(x),y=0,[1,2]	volumeabout\:y=0,y=\ln(x),y=0,[1,2]
(dy)/(dx)=-9.81+0.00375y^2	\frac{dy}{dx}=-9.81+0.00375y^{2}
laplacetransform e^{-3t}cos(-t)	laplacetransform\:e^{-3t}\cos(-t)
integral of 5u^{3/2}	\int\:5u^{\frac{3}{2}}du
derivative of (2x-6/(4-x))	\frac{d}{dx}(\frac{2x-6}{4-x})
integral of (x^2)/((x^3+1)^2)	\int\:\frac{x^{2}}{(x^{3}+1)^{2}}dx
derivative of 9/(sqrt(x+4))	\frac{d}{dx}(\frac{9}{\sqrt{x+4}})
derivative of (2x+5/(7x^2))	\frac{d}{dx}(\frac{2x+5}{7x^{2}})

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