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Popular Calculus Problems

integral of xe^{-x/9}	\int\:xe^{-\frac{x}{9}}dx
integral of 2x+7x^{-2}	\int\:2x+7x^{-2}dx
(d^2)/(dx^2)(8x+15)	\frac{d^{2}}{dx^{2}}(8x+15)
integral from 0 to 3 of (x-1)^2	\int\:_{0}^{3}(x-1)^{2}dx
derivative of 4x^2sin(4x)	\frac{d}{dx}(4x^{2}\sin(4x))
integral of (x+6)/((x^2+6)(x^2+1))	\int\:\frac{x+6}{(x^{2}+6)(x^{2}+1)}dx
limit as x approaches 0 of x+\|x\|	\lim\:_{x\to\:0}(x+\left\|x\right\|)
derivative of e^{4x}+e^{-x}	\frac{d}{dx}(e^{4x}+e^{-x})
(\partial)/(\partial x)((ax+by)/(cx+dy))	\frac{\partial\:}{\partial\:x}(\frac{ax+by}{cx+dy})
derivative of x+1/(sqrt(x))	\frac{d}{dx}(x+\frac{1}{\sqrt{x}})
limit as x approaches-1 of-x^2+4x-8	\lim\:_{x\to\:-1}(-x^{2}+4x-8)
integral of cos^5(3y)	\int\:\cos^{5}(3y)dy
limit as x approaches 0 of (cos(x))/x	\lim\:_{x\to\:0}(\frac{\cos(x)}{x})
limit as y approaches 0 of sin(1/y)	\lim\:_{y\to\:0}(\sin(\frac{1}{y}))
derivative of tan(e^x*cosh(e^x))	\frac{d}{dx}(\tan(e^{x})\cdot\:\cosh(e^{x}))
(d^4)/(dx^4)(ln(x+1))	\frac{d^{4}}{dx^{4}}(\ln(x+1))
(dy)/(dx)=(x+1)	\frac{dy}{dx}=(x+1)
y^{''''}+2*y^{''}+y=0	y^{\prime\:\prime\:\prime\:\prime\:}+2\cdot\:y^{\prime\:\prime\:}+y=0
(\partial)/(\partial y)(2xy+2x)	\frac{\partial\:}{\partial\:y}(2xy+2x)
derivative of sin^2(8x)	\frac{d}{dx}(\sin^{2}(8x))
(dy)/(dx)+xy=xy^2	\frac{dy}{dx}+xy=xy^{2}
derivative of-cos(cos(x)sin(x))	\frac{d}{dx}(-\cos(\cos(x))\sin(x))
integral of x^3sin^2(x)	\int\:x^{3}\sin^{2}(x)dx
integral from pi/4 to pi/3 of 1	\int\:_{\frac{π}{4}}^{\frac{π}{3}}1
(\partial)/(\partial x)(2xy+x^2+3y^2)	\frac{\partial\:}{\partial\:x}(2xy+x^{2}+3y^{2})
xy^'+y=e^x,y(-1)=4	xy^{\prime\:}+y=e^{x},y(-1)=4
d/(dr)(pir^2h)	\frac{d}{dr}(πr^{2}h)
y^{''}+16y=0,y(0)=2,y^'(0)=-2	y^{\prime\:\prime\:}+16y=0,y(0)=2,y^{\prime\:}(0)=-2
(9+2xsin(y))dx-x^2cos(y)dy=0	(9+2x\sin(y))dx-x^{2}\cos(y)dy=0
derivative of 5/((x^2+2^3))	\frac{d}{dx}(\frac{5}{(x^{2}+2)^{3}})
integral of e^{u/v}	\int\:e^{\frac{u}{v}}du
integral of ((u-2)/(sqrt(u)))	\int\:(\frac{u-2}{\sqrt{u}})du
integral of (X^2)/2	\int\:\frac{X^{2}}{2}dX
integral of 3xe^{8x}	\int\:3xe^{8x}dx
derivative of e^x*x^2	\frac{d}{dx}(e^{x}\cdot\:x^{2})
integral of (x^2+2)/(x-1)	\int\:\frac{x^{2}+2}{x-1}dx
integral of (x^{3/2}+4x+4)	\int\:(x^{\frac{3}{2}}+4x+4)dx
derivative of-(64/((1+8x)^2))	\frac{d}{dx}(-\frac{64}{(1+8x)^{2}})
tangent of f(x)=5tan(x),\at x= pi/3	tangent\:f(x)=5\tan(x),\at\:x=\frac{π}{3}
integral of (x+1)/(x-3)	\int\:\frac{x+1}{x-3}dx
(dy)/(dx)=e^{(x-y)}	\frac{dy}{dx}=e^{(x-y)}
limit as x approaches-1-of 4-x	\lim\:_{x\to\:-1-}(4-x)
d/(dt)(e^{-t}(3cos(t/2)+2sin(t/2)))	\frac{d}{dt}(e^{-t}(3\cos(\frac{t}{2})+2\sin(\frac{t}{2})))
(dy)/(dx)=-1/4 e^xy^{-2}	\frac{dy}{dx}=-\frac{1}{4}e^{x}y^{-2}
integral from-1 to 1 of y^2-2-e^y	\int\:_{-1}^{1}y^{2}-2-e^{y}dy
derivative of x^3(2x+1^3)	\frac{d}{dx}(x^{3}(2x+1)^{3})
limit as x approaches 1 of (x+1)/(x^2-1)	\lim\:_{x\to\:1}(\frac{x+1}{x^{2}-1})
integral from 0 to (3pi)/2 of 6\|sin(x)\|	\int\:_{0}^{\frac{3π}{2}}6\left\|\sin(x)\right\|dx
integral of cos^7(1/3)x	\int\:\cos^{7}(\frac{1}{3})xdx
integral of 12x^2-6x	\int\:12x^{2}-6xdx
(\partial)/(\partial x)(2sqrt(xy)-ye^{y/z})	\frac{\partial\:}{\partial\:x}(2\sqrt{xy}-ye^{\frac{y}{z}})
integral of sqrt(1+1/(x^{2/3))}	\int\:\sqrt{1+\frac{1}{x^{\frac{2}{3}}}}dx
limit as x approaches 1 of 5x^2+1	\lim\:_{x\to\:1}(5x^{2}+1)
tangent of y=x^2+4x+9,\at x=8	tangent\:y=x^{2}+4x+9,\at\:x=8
derivative of sqrt(x^2-4)	\frac{d}{dx}(\sqrt{x^{2}-4})
integral from 0 to 1 of 2e^x	\int\:_{0}^{1}2e^{x}dx
limit as x approaches 0-of 2/x	\lim\:_{x\to\:0-}(\frac{2}{x})
x^'=x-2	x^{\prime\:}=x-2
(dy)/(dt)= 1/((2y+1))	\frac{dy}{dt}=\frac{1}{(2y+1)}
laplacetransform 3e^{-2t}+2sin(3t)	laplacetransform\:3\cdot\:e^{-2t}+2\cdot\:\sin(3t)
integral from-16 to 0 of 1/(sqrt(9-x))	\int\:_{-16}^{0}\frac{1}{\sqrt{9-x}}dx
integral of cos(2x)	\int\:\cos(2x)dx
limit as x approaches 0 of (x-15)/(x-5)	\lim\:_{x\to\:0}(\frac{x-15}{x-5})
integral of (4x^5-16x^4+8x^3)/(4x^2)	\int\:\frac{4x^{5}-16x^{4}+8x^{3}}{4x^{2}}dx
derivative of f(x)= 4/5 x^{10}	derivative\:f(x)=\frac{4}{5}x^{10}
integral of (-7x+4)/(x^3)	\int\:\frac{-7x+4}{x^{3}}dx
tangent of 2x^3+6x^2-90x-6	tangent\:2x^{3}+6x^{2}-90x-6
integral of 4sin(x)	\int\:4\sin(x)dx
derivative of x*sqrt(1-x^2)	derivative\:x\cdot\:\sqrt{1-x^{2}}
derivative of 3ln(7x)	\frac{d}{dx}(3\ln(7x))
integral of-e^{3t}	\int\:-e^{3t}dt
derivative of 6x-tan(6x)	\frac{d}{dx}(6x-\tan(6x))
laplacetransform e^{4t}cos(2t)	laplacetransform\:e^{4t}\cos(2t)
limit as x approaches (3pi)/2-of tan(x)	\lim\:_{x\to\:\frac{3π}{2}-}(\tan(x))
derivative of (x^2+2x-7)/((x+1)^2)	derivative\:\frac{x^{2}+2x-7}{(x+1)^{2}}
integral of (((ln(x))^2)/(x^2))	\int\:(\frac{(\ln(x))^{2}}{x^{2}})dx
sum from n=0 to infinity of 3(1/5)^n	\sum\:_{n=0}^{\infty\:}3(\frac{1}{5})^{n}
(\partial)/(\partial x)(z/(x+4y))	\frac{\partial\:}{\partial\:x}(\frac{z}{x+4y})
(\partial)/(\partial x)(xy+z^3x)	\frac{\partial\:}{\partial\:x}(xy+z^{3}x)
integral of e^z	\int\:e^{z}
integral of (2x^2)	\int\:(2x^{2})dx
(\partial)/(\partial x)(y^2-x^3-2x)	\frac{\partial\:}{\partial\:x}(y^{2}-x^{3}-2x)
derivative of y=((x+8))/((x-5))	derivative\:y=\frac{(x+8)}{(x-5)}
taylor (x^2-1)cos(3x)	taylor\:(x^{2}-1)\cos(3x)
limit as x approaches-7+of-(8x)/(x+7)	\lim\:_{x\to\:-7+}(-\frac{8x}{x+7})
derivative of (3x^2/2)	\frac{d}{dx}(\frac{3x^{2}}{2})
derivative of-0.7x^2	derivative\:-0.7x^{2}
tangent of y=6sqrt(x)(9.18)	tangent\:y=6\sqrt{x}(9.18)
derivative of (2x^5+x^2-5/(x^2))	\frac{d}{dx}(\frac{2x^{5}+x^{2}-5}{x^{2}})
limit as x approaches infinity of 2x^2-3x	\lim\:_{x\to\:\infty\:}(2x^{2}-3x)
derivative of axcos(x)	\frac{d}{dx}(ax\cos(x))
integral of sin^5(1)	\int\:\sin^{5}(1)dx
slope ofintercept (-9,7),(-6,-3)	slopeintercept\:(-9,7),(-6,-3)
derivative of (5x+2)(x^3+4x)	derivative\:(5x+2)(x^{3}+4x)
derivative of 12x^2-24x	derivative\:12x^{2}-24x
integral of sqrt(9-r^2)r	\int\:\sqrt{9-r^{2}}rdr
integral of ((sqrt(a)-sqrt(b))^4)/(sqrt(ax))	\int\:\frac{(\sqrt{a}-\sqrt{b})^{4}}{\sqrt{ax}}dx
(dy)/(dx)=4sqrt(yx)	\frac{dy}{dx}=4\sqrt{yx}
tangent of f(x)=8x^2+4,\at x=-7	tangent\:f(x)=8x^{2}+4,\at\:x=-7
derivative of x^3+3x^2+6x	\frac{d}{dx}(x^{3}+3x^{2}+6x)

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