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Popular Calculus Problems

integral of (x^5+7)/(x^2)	\int\:\frac{x^{5}+7}{x^{2}}dx
derivative of 1/(sqrt(4+x^2))	\frac{d}{dx}(\frac{1}{\sqrt{4+x^{2}}})
derivative of sin(x+3cos(x))	\frac{d}{dx}(\sin(x)+3\cos(x))
integral of x^3sqrt(5-x^2)	\int\:x^{3}\sqrt{5-x^{2}}dx
4xy^2+(dy)/(dx)=5x^4y^2	4xy^{2}+\frac{dy}{dx}=5x^{4}y^{2}
integral of (e^y+4)^5e^y	\int\:(e^{y}+4)^{5}e^{y}dy
integral of-2/25 x+45	\int\:-\frac{2}{25}x+45dx
integral from 0 to infinity of x^5e^{-x}	\int\:_{0}^{\infty\:}x^{5}e^{-x}dx
(\partial)/(\partial x)(x^{10}+xy^{11}+9)	\frac{\partial\:}{\partial\:x}(x^{10}+xy^{11}+9)
derivative of cos^2(x^4)	\frac{d}{dx}(\cos^{2}(x^{4}))
integral from 0 to 2 of x/8	\int\:_{0}^{2}\frac{x}{8}dx
(\partial)/(\partial y)(2x-x^3+3xy^2)	\frac{\partial\:}{\partial\:y}(2x-x^{3}+3xy^{2})
integral of (x^2)/(x^2+1)	\int\:\frac{x^{2}}{x^{2}+1}dx
taylor 7xe^x	taylor\:7xe^{x}
integral of cos(8x)cos(5x)	\int\:\cos(8x)\cos(5x)dx
integral of x\sqrt[9]{4+x^2}	\int\:x\sqrt[9]{4+x^{2}}dx
inverse oflaplace (e^{-s})/(s^5)	inverselaplace\:\frac{e^{-s}}{s^{5}}
limit as x approaches 0 of ((4^x-1))/x	\lim\:_{x\to\:0}(\frac{(4^{x}-1)}{x})
integral of sin(7x-10)	\int\:\sin(7x-10)dx
limit as x approaches infinity of 4x^3	\lim\:_{x\to\:\infty\:}(4x^{3})
(\partial}{\partial y}(ln(\frac{x^2)/y))	\frac{\partial\:}{\partial\:y}(\ln(\frac{x^{2}}{y}))
derivative of sqrt(4/9 x^3)	\frac{d}{dx}(\sqrt{\frac{4}{9}x^{3}})
maclaurin xsin(x^2)	maclaurin\:x\sin(x^{2})
integral of sqrt(x-2)x	\int\:\sqrt{x-2}xdx
integral of (8x+13)e^x	\int\:(8x+13)e^{x}dx
tangent of y=x^2+x,\at x=1	tangent\:y=x^{2}+x,\at\:x=1
derivative of arctan(((a^2-x^3)/(b^2)))	\frac{d}{dx}(\arctan(\frac{(a^{2}-x^{3})}{b^{2}}))
derivative of (1-2x^2/(x^4-2x^2+6))	\frac{d}{dx}(\frac{1-2x^{2}}{x^{4}-2x^{2}+6})
integral of sqrt(1+(4x)^2)	\int\:\sqrt{1+(4x)^{2}}dx
integral of 1/(sin(x)cos^2(x))	\int\:\frac{1}{\sin(x)\cos^{2}(x)}dx
tangent of f(x)=10sin(x)+10sqrt(3)cos(x)	tangent\:f(x)=10\sin(x)+10\sqrt{3}\cos(x)
inverse oflaplace 2/(s^2+3s+2)	inverselaplace\:\frac{2}{s^{2}+3s+2}
sum from n=5 to infinity of (n^2)/(n!)	\sum\:_{n=5}^{\infty\:}\frac{n^{2}}{n!}
integral from-1 to 1 of sqrt(1+x^{-2/3)}	\int\:_{-1}^{1}\sqrt{1+x^{-\frac{2}{3}}}dx
limit as t approaches 1 of 1/(t^2-1)	\lim\:_{t\to\:1}(\frac{1}{t^{2}-1})
(f(t)+g(t))\prime	(f(t)+g(t))\prime
integral of sqrt(x^2+6)	\int\:\sqrt{x^{2}+6}dx
integral of x+cos(x)	\int\:x+\cos(x)dx
derivative of 2xsec(x)	\frac{d}{dx}(2x\sec(x))
derivative of (x+2^x)	\frac{d}{dx}((x+2)^{x})
integral of ((2+e^x)^2)/(e^x)	\int\:\frac{(2+e^{x})^{2}}{e^{x}}dx
xy^'+3y=x^4-x	xy^{\prime\:}+3y=x^{4}-x
integral of (e^x)/((5-e^x)^2)	\int\:\frac{e^{x}}{(5-e^{x})^{2}}dx
integral of 1/(v^2-v+1)	\int\:\frac{1}{v^{2}-v+1}dv
derivative of f(x)=ln((x+1)/(x-1))	derivative\:f(x)=\ln(\frac{x+1}{x-1})
integral of 1/(x^2sqrt(1-x^2))	\int\:\frac{1}{x^{2}\sqrt{1-x^{2}}}dx
derivative of 5x^2+4x+2	derivative\:5x^{2}+4x+2
y^{''}+2y^'+2y=sin(ax)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(ax)
tangent of 2x^3+3x^2-12x+5	tangent\:2x^{3}+3x^{2}-12x+5
(dy)/(dx)-(2xy)/(x^2+1)=1	\frac{dy}{dx}-\frac{2xy}{x^{2}+1}=1
(d^2y)/(dx^2)-49y=e^{7x}	\frac{d^{2}y}{dx^{2}}-49y=e^{7x}
integral of x/(sqrt(8-2x^2-x^4))	\int\:\frac{x}{\sqrt{8-2x^{2}-x^{4}}}dx
derivative of y=\sqrt[5]{x}	derivative\:y=\sqrt[5]{x}
integral of x\sqrt[3]{x+1}	\int\:x\sqrt[3]{x+1}dx
integral of sin(7x)	\int\:\sin(7x)dx
y^{''}+4y=4t	y^{\prime\:\prime\:}+4y=4t
derivative of f(x)=(7^{-3x})	derivative\:f(x)=(7^{-3x})
integral of (4x^2-2/x)	\int\:(4x^{2}-\frac{2}{x})dx
derivative of f(x)=-x^2+1	derivative\:f(x)=-x^{2}+1
integral of sqrt(1+4x^2)	\int\:\sqrt{1+4x^{2}}dx
integral of x^2e^{x/2}	\int\:x^{2}e^{\frac{x}{2}}dx
integral of (3ln(x))/(x^2)	\int\:\frac{3\ln(x)}{x^{2}}dx
integral of (y^2)/y	\int\:\frac{y^{2}}{y}dy
integral of sin^3(x)cos^{14}(x)	\int\:\sin^{3}(x)\cos^{14}(x)dx
limit as a approaches-1 of a	\lim\:_{a\to\:-1}(a)
integral of (1/(x(2x^2-x+1)(x+1)))	\int\:(\frac{1}{x(2x^{2}-x+1)(x+1)})dx
slope of (1,2),(-1,-2)	slope\:(1,2),(-1,-2)
tangent of y=x+sqrt(x),(1,2)	tangent\:y=x+\sqrt{x},(1,2)
derivative of (8x^2+6x+4/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+6x+4}{\sqrt{x}})
(d^2)/(dx^2)(5sec(x))	\frac{d^{2}}{dx^{2}}(5\sec(x))
derivative of f(x)=6e^{x^{-5}}	derivative\:f(x)=6e^{x^{-5}}
2ydx+3xdy=0	2ydx+3xdy=0
integral of e^{2x}2	\int\:e^{2x}2dx
normal of y=x^2-3x,(5,10)	normal\:y=x^{2}-3x,(5,10)
integral of sec(38x)tan(38x)	\int\:\sec(38x)\tan(38x)dx
derivative of 3^4	\frac{d}{dx}(3^{4})
integral of (3x-2)	\int\:(3x-2)dx
d/(du)(u+v)	\frac{d}{du}(u+v)
integral of 12log_{11}(x)	\int\:12\log_{11}(x)dx
integral of ((3-x)(5+x))/(x^4)	\int\:\frac{(3-x)(5+x)}{x^{4}}dx
derivative of f(x)=(e^{3x})/(x^6)	derivative\:f(x)=\frac{e^{3x}}{x^{6}}
(5x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=4	(5x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0,y(1)=4
y^'+2xy=x^2	y^{\prime\:}+2xy=x^{2}
derivative of f(x)=(4x^3-2x+1)/(x^2)	derivative\:f(x)=\frac{4x^{3}-2x+1}{x^{2}}
limit as x approaches+6 of 3	\lim\:_{x\to\:+6}(3)
integral of x(1-x)^2	\int\:x(1-x)^{2}dx
limit as x approaches-2 of x^2+5x+4	\lim\:_{x\to\:-2}(x^{2}+5x+4)
integral of (x+2)/(x+1)	\int\:\frac{x+2}{x+1}dx
derivative of 2(3x^2+x-3^2)	\frac{d}{dx}(2(3x^{2}+x-3)^{2})
integral of (x^2-4)/(x^2)	\int\:\frac{x^{2}-4}{x^{2}}dx
limit as x approaches 1 of (x-2)/(x^2-4)	\lim\:_{x\to\:1}(\frac{x-2}{x^{2}-4})
derivative of y=(4x-9)/(2x+3),x=2	derivative\:y=\frac{4x-9}{2x+3},x=2
integral from 0 to 4 of xe^x	\int\:_{0}^{4}xe^{x}dx
(ln(x^2+1))^'	(\ln(x^{2}+1))^{\prime\:}
y^{''}-3y^'+2y=0,y(-1)=0,y^'(-1)=1	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=0,y(-1)=0,y^{\prime\:}(-1)=1
integral of (3x+5)/(sqrt(x(2x-1)))	\int\:\frac{3x+5}{\sqrt{x(2x-1)}}dx
derivative of t^3e^tt	derivative\:t^{3}e^{t}t
limit as n approaches infinity of c^n	\lim\:_{n\to\:\infty\:}(c^{n})
y^{''}+y^'-2y=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}+y^{\prime\:}-2y=0,y(0)=1,y^{\prime\:}(0)=1
(3cos(t))^'	(3\cos(t))^{\prime\:}

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