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Popular Calculus Problems

integral of (sin(2x))/(14+cos^2(x))	\int\:\frac{\sin(2x)}{14+\cos^{2}(x)}dx
y^'+2/x y=y^2,y(1)=3	y^{\prime\:}+\frac{2}{x}y=y^{2},y(1)=3
derivative of a/(2y)	\frac{d}{dx}(\frac{a}{2y})
t^3y^'+4t^2y=0	t^{3}y^{\prime\:}+4t^{2}y=0
integral of (3sin^3(x))/(cos(x))	\int\:\frac{3\sin^{3}(x)}{\cos(x)}dx
(\partial)/(\partial x)(2x^2+3y^2+z^2)	\frac{\partial\:}{\partial\:x}(2x^{2}+3y^{2}+z^{2})
derivative of (2x+1/(x-3))	\frac{d}{dx}(\frac{2x+1}{x-3})
derivative of sin(ln(3x^2+x))	\frac{d}{dx}(\sin(\ln(3x^{2}+x)))
derivative of-(10/(10-x))	\frac{d}{dx}(-\frac{10}{10-x})
integral of 1/(x*sqrt(1-x^2))	\int\:\frac{1}{x\cdot\:\sqrt{1-x^{2}}}dx
derivative of axe^{2x}	\frac{d}{dx}(axe^{2x})
tangent of f(x)=x^3+x^2+(6/x),\at x=1	tangent\:f(x)=x^{3}+x^{2}+(\frac{6}{x}),\at\:x=1
tangent of y=(x-4)^2,\at x=5	tangent\:y=(x-4)^{2},\at\:x=5
(dy)/(dt)=-2y+10	\frac{dy}{dt}=-2y+10
integral of x^3(x^4-1)^5	\int\:x^{3}(x^{4}-1)^{5}dx
tangent of y=4e^xcos(x),(0,4)	tangent\:y=4e^{x}\cos(x),(0,4)
(\partial)/(\partial x)(xe^y+ln(x)y)	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{y}+\ln(x)\cdot\:y)
derivative of v/(v+c/v)	derivative\:\frac{v}{v+\frac{c}{v}}
integral from 0 to 1 of e^{-5x^2}	\int\:_{0}^{1}e^{-5x^{2}}dx
limit as x approaches infinity of e^{1/2-1/(x^2)}-1	\lim\:_{x\to\:\infty\:}(e^{\frac{1}{2}-\frac{1}{x^{2}}}-1)
sum from n=1 to infinity of 1(1/6)^n	\sum\:_{n=1}^{\infty\:}1(\frac{1}{6})^{n}
sum from n=1 to infinity of n^n(x-3)^n	\sum\:_{n=1}^{\infty\:}n^{n}(x-3)^{n}
integral from 0 to pi/2 of (cos(θ))/(sqrt(1+sin(θ)))	\int\:_{0}^{\frac{π}{2}}\frac{\cos(θ)}{\sqrt{1+\sin(θ)}}dθ
sum from n=0 to infinity of 2((-2)/3)^n	\sum\:_{n=0}^{\infty\:}2(\frac{-2}{3})^{n}
(dy)/(dx)=e^{-(x+y)}	\frac{dy}{dx}=e^{-(x+y)}
integral of e^{-x+2}	\int\:e^{-x+2}dx
area y=4(x+1),y=5(x+1),x=5	area\:y=4(x+1),y=5(x+1),x=5
derivative of f(x)=9sin(x)cos(x)	derivative\:f(x)=9\sin(x)\cos(x)
integral of sin(x)cos(2x)	\int\:\sin(x)\cos(2x)dx
taylor cos(x^3)	taylor\:\cos(x^{3})
integral from 1 to infinity of 5e^{-5x}	\int\:_{1}^{\infty\:}5e^{-5x}dx
integral of e^{-x^2}	\int\:e^{-x^{2}}dx
integral of ((2z))/(\sqrt[3]{z^2+1)}	\int\:\frac{(2z)}{\sqrt[3]{z^{2}+1}}dz
derivative of e^{x^2-x+1}	\frac{d}{dx}(e^{x^{2}-x+1})
derivative of x^4+4x^3-2x^2-12x	\frac{d}{dx}(x^{4}+4x^{3}-2x^{2}-12x)
derivative of 10^{-2x}	\frac{d}{dx}(10^{-2x})
integral of (x^2)/(sqrt(2x-1))	\int\:\frac{x^{2}}{\sqrt{2x-1}}dx
inverse oflaplace 8/((9s^2+12s+4)(s))	inverselaplace\:\frac{8}{(9s^{2}+12s+4)(s)}
integral of x*e^{x^2}	\int\:x\cdot\:e^{x^{2}}dx
(d^2x)/(dt^2)+9x=-sin(3t)	\frac{d^{2}x}{dt^{2}}+9x=-\sin(3t)
(\partial}{\partial x}(ln(\frac{2xy)/z))	\frac{\partial\:}{\partial\:x}(\ln(\frac{2xy}{z}))
integral of (5x)/(3x^{1/3)}	\int\:\frac{5x}{3x^{\frac{1}{3}}}dx
integral from-1 to 1 of (\sqrt[3]{t-2})	\int\:_{-1}^{1}(\sqrt[3]{t-2})dt
tangent of y=1.1x+e^x,(0,1)	tangent\:y=1.1x+e^{x},(0,1)
volumeabout y=0,y=x^2,y=4x-x^2,[0,2]	volumeabout\:y=0,y=x^{2},y=4x-x^{2},[0,2]
(1+cos(t))y^'=(1+e^{-y})sin(t),y(0)=0	(1+\cos(t))y^{\prime\:}=(1+e^{-y})\sin(t),y(0)=0
derivative of (x^2+5)(8-x)	derivative\:(x^{2}+5)(8-x)
integral of (2x)/(1+4x^2)	\int\:\frac{2x}{1+4x^{2}}dx
derivative of 6/(x^3)	derivative\:\frac{6}{x^{3}}
integral of (3x^2)/(4sqrt(5-x^3))	\int\:\frac{3x^{2}}{4\sqrt{5-x^{3}}}dx
tangent of f(x)=3x^2-3x,\at x=3	tangent\:f(x)=3x^{2}-3x,\at\:x=3
limit as x approaches 0 of (sinh(x))/x	\lim\:_{x\to\:0}(\frac{\sinh(x)}{x})
derivative of (6x^2+2x+4)/(sqrt(x))	derivative\:\frac{6x^{2}+2x+4}{\sqrt{x}}
y^{''}+3y^'-2y=0	y^{\prime\:\prime\:}+3y^{\prime\:}-2y=0
(dy)/(dx)=4e^{x-y}	\frac{dy}{dx}=4e^{x-y}
(xy+y^2+y)dx+(x+2y)dy=0	(xy+y^{2}+y)dx+(x+2y)dy=0
y^'=cos(x+y)	y^{\prime\:}=\cos(x+y)
(\partial)/(\partial x)(e^xcos(x+y))	\frac{\partial\:}{\partial\:x}(e^{x}\cos(x+y))
derivative of sec(pi/3)	derivative\:\sec(\frac{π}{3})
integral of sec^4(x/4)	\int\:\sec^{4}(\frac{x}{4})dx
derivative of 5/((x-6^2))	\frac{d}{dx}(\frac{5}{(x-6)^{2}})
integral from 1/5 to 3 of 8xln(5x)	\int\:_{\frac{1}{5}}^{3}8x\ln(5x)dx
derivative of ln(e)	derivative\:\ln(e)
integral of x^{3/4}	\int\:x^{\frac{3}{4}}dx
y^{''}+289y=sec(17x)	y^{\prime\:\prime\:}+289y=\sec(17x)
derivative of f(x)=2x^5-3e^{6x}	derivative\:f(x)=2x^{5}-3e^{6x}
integral from 0 to 1 of x^2-sqrt(x)	\int\:_{0}^{1}x^{2}-\sqrt{x}dx
tangent of-2x^5+4x^4	tangent\:-2x^{5}+4x^{4}
derivative of (12/x-4/(x^3)+1/(x^4))	\frac{d}{dx}(\frac{12}{x}-\frac{4}{x^{3}}+\frac{1}{x^{4}})
y^{''}+2y^'+y=0,y(2)=1,y^'(2)=-2	y^{\prime\:\prime\:}+2y^{\prime\:}+y=0,y(2)=1,y^{\prime\:}(2)=-2
integral of ((x^2-x+1))/((x^2+x))	\int\:\frac{(x^{2}-x+1)}{(x^{2}+x)}dx
derivative of 11sqrt(x)-6/x	\frac{d}{dx}(11\sqrt{x}-\frac{6}{x})
integral of t^6e^{-t^7}	\int\:t^{6}e^{-t^{7}}dt
integral of 1/(v^2-1)	\int\:\frac{1}{v^{2}-1}dv
derivative of ln(sqrt(x)-1)	\frac{d}{dx}(\ln(\sqrt{x}-1))
integral of 1/(sqrt(x)(1-2\sqrt{x))}	\int\:\frac{1}{\sqrt{x}(1-2\sqrt{x})}dx
derivative of y= 7/(ln(x))	derivative\:y=\frac{7}{\ln(x)}
derivative of (5x/6)	\frac{d}{dx}(\frac{5x}{6})
limit as x approaches 9-of 1/(x-9)	\lim\:_{x\to\:9-}(\frac{1}{x-9})
limit as x approaches 0+of x[ln(x)]^2	\lim\:_{x\to\:0+}(x[\ln(x)]^{2})
derivative of 2^{5x}3^{4x^2}	\frac{d}{dx}(2^{5x}3^{4x^{2}})
(dy)/(dx)=(x-4)/(y+5)	\frac{dy}{dx}=\frac{x-4}{y+5}
tangent of f(x)= 2/x ,(6, 1/3)	tangent\:f(x)=\frac{2}{x},(6,\frac{1}{3})
integral of 15ln(x+5)	\int\:15\ln(x+5)dx
derivative of 7e^x+8/(\sqrt[3]{x)}	derivative\:7e^{x}+\frac{8}{\sqrt[3]{x}}
integral of (x^2+5x-1)/(x^3)	\int\:\frac{x^{2}+5x-1}{x^{3}}dx
integral of (-3x+2)e-x	\int\:(-3x+2)e-xdx
limit as x approaches 1 of (\sqrt[4]{x}-1)/(\sqrt[5]{x)-1}	\lim\:_{x\to\:1}(\frac{\sqrt[4]{x}-1}{\sqrt[5]{x}-1})
limit as x approaches 3 of ((x^{2-7x+12}))/((3-x))	\lim\:_{x\to\:3}(\frac{(x^{2-7x+12})}{(3-x)})
integral of y/((y+1)^2)	\int\:\frac{y}{(y+1)^{2}}dy
limit as x approaches infinity of-2xe^{-2x}	\lim\:_{x\to\:\infty\:}(-2xe^{-2x})
derivative of y= 1/(2cos^2(x))	derivative\:y=\frac{1}{2\cos^{2}(x)}
sum from i=0 to infinity of i/(2^i)	\sum\:_{i=0}^{\infty\:}\frac{i}{2^{i}}
(dy}{dx}=\frac{x^3)/y	\frac{dy}{dx}=\frac{x^{3}}{y}
integral of x/((x+1)^8)	\int\:\frac{x}{(x+1)^{8}}dx
integral of (e^{5x})/(e^{5x)+4}	\int\:\frac{e^{5x}}{e^{5x}+4}dx
(\partial)/(\partial y)(pix^2y)	\frac{\partial\:}{\partial\:y}(πx^{2}y)
integral of 21x^2ln(x)	\int\:21x^{2}\ln(x)dx
(dy)/(dt)=te^{2y}	\frac{dy}{dt}=te^{2y}
integral of xln(3x^2)	\int\:x\ln(3x^{2})dx

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