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Popular Calculus Problems

integral of-3sqrt(x+2x)	\int\:-3\sqrt{x+2x}dx
sum from n=0 to infinity of (2x+5)^n	\sum\:_{n=0}^{\infty\:}(2x+5)^{n}
derivative of 5x^2-x^3	derivative\:5x^{2}-x^{3}
limit as x approaches 0 of ln(1-7x)	\lim\:_{x\to\:0}(\ln(1-7x))
area x=y^2,x=81	area\:x=y^{2},x=81
(\partial)/(\partial y)(2xe^{xy})	\frac{\partial\:}{\partial\:y}(2xe^{xy})
(\partial)/(\partial x)(2xyz+xy^2+xz)	\frac{\partial\:}{\partial\:x}(2xyz+xy^{2}+xz)
derivative of (4x)/(x+2)	derivative\:\frac{4x}{x+2}
limit as x approaches o of (cos(x))/x	\lim\:_{x\to\:o}(\frac{\cos(x)}{x})
derivative of arccos((1-x/(1+x)))	\frac{d}{dx}(\arccos(\frac{1-x}{1+x}))
integral of (3x^2)/(\sqrt[3]{x^3+1)}	\int\:\frac{3x^{2}}{\sqrt[3]{x^{3}+1}}dx
x(dy)/(dx)-2y=3x^2+2x	x\cdot\:\frac{dy}{dx}-2\cdot\:y=3\cdot\:x^{2}+2\cdot\:x
(\partial)/(\partial y)(arctan(y^3x))	\frac{\partial\:}{\partial\:y}(\arctan(y^{3}x))
integral of 1/(sqrt(1+x^2))	\int\:\frac{1}{\sqrt{1+x^{2}}}dx
derivative of y=sin(arccos(t))	derivative\:y=\sin(\arccos(t))
derivative of (15/(x^2))	\frac{d}{dx}(\frac{15}{x^{2}})
integral from 0 to 12 of 1/(36-x^2)	\int\:_{0}^{12}\frac{1}{36-x^{2}}dx
integral from 0 to pi/6 of tsin(2t)	\int\:_{0}^{\frac{π}{6}}t\sin(2t)dt
inverse oflaplace 4/(s^2(s+2))+3/(s+2)	inverselaplace\:\frac{4}{s^{2}(s+2)}+\frac{3}{s+2}
derivative of arctan(x/(4-sqrt(16-x^2)))	\frac{d}{dx}(\arctan(\frac{x}{4-\sqrt{16-x^{2}}}))
limit as x approaches 1 of (2x)/(6x-10)	\lim\:_{x\to\:1}(\frac{2x}{6x-10})
derivative of 60	\frac{d}{dx}(60)
tangent of xsqrt(x)(9.27)	tangent\:x\sqrt{x}(9.27)
integral of (2x^2+3)/(x(x-1)^2)	\int\:\frac{2x^{2}+3}{x(x-1)^{2}}dx
integral of ((3x+4))/(x+3)	\int\:\frac{(3x+4)}{x+3}dx
(\partial}{\partial y}(\frac{(x-y))/x)	\frac{\partial\:}{\partial\:y}(\frac{(x-y)}{x})
y'=y^3-y	y\prime\:=y^{3}-y
derivative of 3x^4+1/(3x^4+3/(2x^2))	\frac{d}{dx}(3x^{4}+\frac{1}{3x^{4}}+\frac{3}{2x^{2}})
derivative of arcsin((3x/4))	\frac{d}{dx}(\arcsin(\frac{3x}{4}))
(dx)/(dt)= 5/(xe^{t+5x)}	\frac{dx}{dt}=\frac{5}{xe^{t+5x}}
integral from-5 to-2 of 4x^3	\int\:_{-5}^{-2}4x^{3}dx
(\partial)/(\partial x)(5x^2y^2)	\frac{\partial\:}{\partial\:x}(5x^{2}y^{2})
derivative of f(x)=5cos^2(x)	derivative\:f(x)=5\cos^{2}(x)
limit as x approaches 4 of (x+4)/(x-3)	\lim\:_{x\to\:4}(\frac{x+4}{x-3})
integral of ((3-7x+9x^2e^{7x})/(x^2))	\int\:(\frac{3-7x+9x^{2}e^{7x}}{x^{2}})dx
integral from 0 to 5 of 100-10t	\int\:_{0}^{5}100-10tdt
normal of f(x)=-761/12 x^4+2089/3 x^3-31015/12 x^2+11432/3 x-1833,\at x=5.35	normal\:f(x)=-\frac{761}{12}x^{4}+\frac{2089}{3}x^{3}-\frac{31015}{12}x^{2}+\frac{11432}{3}x-1833,\at\:x=5.35
integral of (5x^2-3x+18)/(9x-x^3)	\int\:\frac{5x^{2}-3x+18}{9x-x^{3}}dx
derivative of e^{ax}+arctan(cx)	\frac{d}{dx}(e^{ax}+\arctan(cx))
derivative of y= 7/(3x^4)	derivative\:y=\frac{7}{3x^{4}}
integral of (x^3)/((a^2+x^2)^2)	\int\:\frac{x^{3}}{(a^{2}+x^{2})^{2}}dx
limit as x approaches-1-of (x^2)/(1+x^3)	\lim\:_{x\to\:-1-}(\frac{x^{2}}{1+x^{3}})
integral from-2 to 4 of 1/2	\int\:_{-2}^{4}\frac{1}{2}dx
derivative of e^{-2x}cos(4x)	\frac{d}{dx}(e^{-2x}\cos(4x))
derivative of ce^x	\frac{d}{dx}(ce^{x})
tangent of f(x)=5x^2-x^3,\at x=1	tangent\:f(x)=5x^{2}-x^{3},\at\:x=1
derivative of 2sin(2v)-4sin^9(2v)	derivative\:2\sin(2v)-4\sin^{9}(2v)
derivative of xe^{-y}	\frac{d}{dx}(xe^{-y})
integral from-2 to-1 of 2/(x^2)	\int\:_{-2}^{-1}\frac{2}{x^{2}}dx
(4x+2x^{-1}y+2x^{-1}y^2)dx+(1+2y)dy=0	(4x+2x^{-1}y+2x^{-1}y^{2})dx+(1+2y)dy=0
derivative of f(x)= x/((1+x^2))	derivative\:f(x)=\frac{x}{(1+x^{2})}
2ydx-xdy=0	2ydx-xdy=0
derivative of x^2-6x+10	derivative\:x^{2}-6x+10
limit as x approaches 1 of sqrt(x+3)	\lim\:_{x\to\:1}(\sqrt{x+3})
derivative of y=xe^{sin(x)}	derivative\:y=xe^{\sin(x)}
(\partial)/(\partial x)(x^3+x^2y^2+y^3)	\frac{\partial\:}{\partial\:x}(x^{3}+x^{2}y^{2}+y^{3})
y^'=5y^2	y^{\prime\:}=5y^{2}
derivative of y=sqrt(25-x-9x^2)	derivative\:y=\sqrt{25-x-9x^{2}}
derivative of (x^2-5^3)	\frac{d}{dx}((x^{2}-5)^{3})
limit as x approaches-3 of+(f(x))	\lim\:_{x\to\:-3}(+(f(x)))
maclaurin e^θ	maclaurin\:e^{θ}
derivative of cot(pix)	\frac{d}{dx}(\cot(π)x)
integral of (x^2)/(\sqrt[3]{(x^3+1)^5)}	\int\:\frac{x^{2}}{\sqrt[3]{(x^{3}+1)^{5}}}dx
f(x)=3e^{3x}	f(x)=3e^{3x}
integral of (sin(2x))/(3+cos(2x))	\int\:\frac{\sin(2x)}{3+\cos(2x)}dx
laplacetransform 1+6t	laplacetransform\:1+6t
extreme f(x)=\sqrt[5]{x}-5e^t	extreme\:f(x)=\sqrt[5]{x}-5e^{t}
derivative of (x^2+16/x)	\frac{d}{dx}(\frac{x^{2}+16}{x})
derivative of (x^3-x-2/(-2x))	\frac{d}{dx}(\frac{x^{3}-x-2}{-2x})
derivative of f(x)=(40x^5)/(e^x)	derivative\:f(x)=\frac{40x^{5}}{e^{x}}
integral of (e^x)/(5+e^x)	\int\:\frac{e^{x}}{5+e^{x}}dx
sum from n=1 to infinity of (n^5)/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{n^{5}}{4^{n}}
integral from 2 to infinity of 0	\int\:_{2}^{\infty\:}0dx
integral of-Fx-x	\int\:-Fx-xdx
integral of (cos(θ))/(sin^2(θ))	\int\:\frac{\cos(θ)}{\sin^{2}(θ)}dθ
(\partial)/(\partial x)((2x-2y)/(y^2+4x^2))	\frac{\partial\:}{\partial\:x}(\frac{2x-2y}{y^{2}+4x^{2}})
integral of x^2sin(ax)	\int\:x^{2}\sin(ax)dx
derivative of 9/(r^3)	derivative\:\frac{9}{r^{3}}
area y=x^2+5x,y=3-x^2	area\:y=x^{2}+5x,y=3-x^{2}
derivative of f(x)=sqrt(x+2)	derivative\:f(x)=\sqrt{x+2}
tangent of sqrt(5x+11)	tangent\:\sqrt{5x+11}
derivative of f(x)=x^2+5x-2	derivative\:f(x)=x^{2}+5x-2
area y=-x^2+x+6,y=4	area\:y=-x^{2}+x+6,y=4
derivative of 3/(x-3)	derivative\:\frac{3}{x-3}
integral of 1/(r^2-2r-3)	\int\:\frac{1}{r^{2}-2r-3}dr
integral from 2 to x of sin(t^4)	\int\:_{2}^{x}\sin(t^{4})dt
integral from 0 to 3 of ln(x^2+1)	\int\:_{0}^{3}\ln(x^{2}+1)dx
limit as t approaches 1 of (sin(3t)-3)/t	\lim\:_{t\to\:1}(\frac{\sin(3t)-3}{t})
limit as x approaches infinity of (9)^x	\lim\:_{x\to\:\infty\:}((9)^{x})
laplacetransform f(t)=4t^2cos(2t)+5te^{-7t}	laplacetransform\:f(t)=4t^{2}\cos(2t)+5te^{-7t}
derivative of 1/(9x^2)	derivative\:\frac{1}{9x^{2}}
derivative of (x^3+2x+7)(2+1/(x^2))	derivative\:(x^{3}+2x+7)(2+\frac{1}{x^{2}})
tangent of x^4-18x^2+81	tangent\:x^{4}-18x^{2}+81
integral of (x^2)/y	\int\:\frac{x^{2}}{y}dx
(dy)/(dx)=(3ex-9e-x)^2	\frac{dy}{dx}=(3ex-9e-x)^{2}
integral from 1 to 2 of 7/(x^2)	\int\:_{1}^{2}\frac{7}{x^{2}}dx
(dy)/(dx)=3x^{-2}e^{-y}	\frac{dy}{dx}=3x^{-2}e^{-y}
integral of ((x^2+9x+1))/((x^2+1)^2)	\int\:\frac{(x^{2}+9x+1)}{(x^{2}+1)^{2}}dx
x^2y^{''}+4xy^'-4y=0,y(1)=0,y^'(1)=3	x^{2}y^{\prime\:\prime\:}+4xy^{\prime\:}-4y=0,y(1)=0,y^{\prime\:}(1)=3
integral of (225)/(x^3-15x^2)	\int\:\frac{225}{x^{3}-15x^{2}}dx

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