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Popular Calculus Problems

y^'= y/x+xe^x	y^{\prime\:}=\frac{y}{x}+xe^{x}
integral of 2/(x^2(x^2+25))	\int\:\frac{2}{x^{2}(x^{2}+25)}dx
(\partial)/(\partial y)(6xy-6y)	\frac{\partial\:}{\partial\:y}(6xy-6y)
(\partial)/(\partial y)(2xy^3-1)	\frac{\partial\:}{\partial\:y}(2xy^{3}-1)
integral of x^32^{-x}	\int\:x^{3}2^{-x}dx
integral of 4/5 sec(x)tan(x)	\int\:\frac{4}{5}\sec(x)\tan(x)dx
limit as x approaches 0 of x^4cos(x/2)	\lim\:_{x\to\:0}(x^{4}\cos(\frac{x}{2}))
derivative of sin(6θ)	derivative\:\sin(6θ)
tangent of y=(-4x)/(x^2+1),(-1,2)	tangent\:y=\frac{-4x}{x^{2}+1},(-1,2)
limit as θ approaches 0 of (sin(5θ))/(θ+tan(7θ))	\lim\:_{θ\to\:0}(\frac{\sin(5θ)}{θ+\tan(7θ)})
integral of (z+1)sqrt(3z+2)	\int\:(z+1)\sqrt{3z+2}dz
integral of 10xsec(x)tan(x)	\int\:10x\sec(x)\tan(x)dx
(\partial)/(\partial x)(ln(2x+3y+6z))	\frac{\partial\:}{\partial\:x}(\ln(2x+3y+6z))
integral of x^{-0.1}	\int\:x^{-0.1}dx
derivative of (ln(x)/(x^6))	\frac{d}{dx}(\frac{\ln(x)}{x^{6}})
derivative of 2sqrt(x-2)	\frac{d}{dx}(2\sqrt{x-2})
integral of (sqrt(x^2-484))/x	\int\:\frac{\sqrt{x^{2}-484}}{x}dx
integral from 1 to 3 of (x^2+2x-3)	\int\:_{1}^{3}(x^{2}+2x-3)dx
integral of x^3arcsin(x)	\int\:x^{3}\arcsin(x)dx
derivative of 2.5sqrt(x^2+0.36)+4(1.1-x)	derivative\:2.5\sqrt{x^{2}+0.36}+4(1.1-x)
integral of (x+4)/(x^2+9x-10)	\int\:\frac{x+4}{x^{2}+9x-10}dx
derivative of f(x)=-2/(x^3)	derivative\:f(x)=-\frac{2}{x^{3}}
sum from n=0 to infinity of (n/(n+2))^2	\sum\:_{n=0}^{\infty\:}(\frac{n}{n+2})^{2}
integral of x\sqrt[8]{64+x^2}	\int\:x\sqrt[8]{64+x^{2}}dx
integral of 23tan^5(x)sec^4(x)	\int\:23\tan^{5}(x)\sec^{4}(x)dx
integral of (2sin(x)-sec^2(x))	\int\:(2\sin(x)-\sec^{2}(x))dx
derivative of 4e^{10x}	derivative\:4e^{10x}
derivative of y=2e^{-2x}	derivative\:y=2e^{-2x}
integral of 1/(w^5)	\int\:\frac{1}{w^{5}}dw
(y^2+9)dx-1/((2x-5)^2)dy=0	(y^{2}+9)dx-\frac{1}{(2x-5)^{2}}dy=0
derivative of 11	\frac{d}{dx}(11)
derivative of f(x)=sqrt(x)+6\sqrt[3]{x}	derivative\:f(x)=\sqrt{x}+6\sqrt[3]{x}
derivative of 3e^x+xe^x	\frac{d}{dx}(3e^{x}+xe^{x})
integral of e^{cos(t)}sin(2t)	\int\:e^{\cos(t)}\sin(2t)dt
derivative of 6/(9-x)	derivative\:\frac{6}{9-x}
integral of cos(v)	\int\:\cos(v)dv
integral of 7sin^3(x)cos(x)	\int\:7\sin^{3}(x)\cos(x)dx
derivative of 1/6 ln(e^{2x}-e^x+1)	\frac{d}{dx}(\frac{1}{6}\ln(e^{2x}-e^{x}+1))
derivative of xsqrt(h(x))	derivative\:x\sqrt{h(x)}
inverse oflaplace 1/(s^2(s^2+2^2))	inverselaplace\:\frac{1}{s^{2}(s^{2}+2^{2})}
y^'+6xy=0	y^{\prime\:}+6xy=0
derivative of f(x)=(4x^2-6x)e^x	derivative\:f(x)=(4x^{2}-6x)e^{x}
laplacetransform 2t-e^{-3t}	laplacetransform\:2t-e^{-3t}
integral of (x^2e^{3x})	\int\:(x^{2}e^{3x})dx
tangent of y= 4/(sqrt(x)),(49, 4/7)	tangent\:y=\frac{4}{\sqrt{x}},(49,\frac{4}{7})
(\partial)/(\partial v)(1/3 (u+v))	\frac{\partial\:}{\partial\:v}(\frac{1}{3}(u+v))
integral of (x/6)^6	\int\:(\frac{x}{6})^{6}dx
d/(dz)(4-z)	\frac{d}{dz}(4-z)
derivative of ln((x+3/(x^2)))	\frac{d}{dx}(\ln(\frac{x+3}{x^{2}}))
y^{''}+2y^'=sin(sqrt(2)t)	y^{\prime\:\prime\:}+2y^{\prime\:}=\sin(\sqrt{2}t)
sum from n=1 to infinity of (3n)/(n+2)	\sum\:_{n=1}^{\infty\:}\frac{3n}{n+2}
integral of x^3*sin(3x)	\int\:x^{3}\cdot\:\sin(3x)dx
integral from 0 to 3 of (5x-x^2)-(2x)	\int\:_{0}^{3}(5x-x^{2})-(2x)dx
(d^2)/(dx^2)(-(2x^2)/(5y^2))	\frac{d^{2}}{dx^{2}}(-\frac{2x^{2}}{5y^{2}})
(dy)/(dx)=e^{6y+10x}	\frac{dy}{dx}=e^{6y+10x}
derivative of 2x-(16/(x^2))	\frac{d}{dx}(2x-\frac{16}{x^{2}})
sum from n=3 to infinity of e^{7-6n}	\sum\:_{n=3}^{\infty\:}e^{7-6n}
integral of (-cos(4x)sin(4x))/4	\int\:\frac{-\cos(4x)\sin(4x)}{4}dx
integral from 0 to 6 of 2x+1	\int\:_{0}^{6}2x+1dx
d/(dt)(-t)	\frac{d}{dt}(-t)
x^2-2xy+x(dy)/(dx)=0	x^{2}-2xy+x\frac{dy}{dx}=0
inverse oflaplace 2/(s^2(s^2+5))	inverselaplace\:\frac{2}{s^{2}(s^{2}+5)}
(d^2)/(dx^2)(16x^3-34x^2)	\frac{d^{2}}{dx^{2}}(16x^{3}-34x^{2})
derivative of (e^x/(6x))	\frac{d}{dx}(\frac{e^{x}}{6x})
derivative of xy= derivative of 4	\frac{d}{dx}(xy)=\frac{d}{dx}(4)
derivative of f(x)=(arccos(x))^3	derivative\:f(x)=(\arccos(x))^{3}
integral of cos(3x+2)	\int\:\cos(3x+2)dx
tangent of f(x)=4(x-1/x)^3,\at x=2	tangent\:f(x)=4(x-\frac{1}{x})^{3},\at\:x=2
tangent of y=(-2x)/(x^2+1),(0,0)	tangent\:y=\frac{-2x}{x^{2}+1},(0,0)
area f(x)=-5/(x^3),y=0,x=-4,x=-1	area\:f(x)=-\frac{5}{x^{3}},y=0,x=-4,x=-1
limit as x approaches 0 of x/(csc^2(x))	\lim\:_{x\to\:0}(\frac{x}{\csc^{2}(x)})
limit as x approaches 5 of x^2-2x+1	\lim\:_{x\to\:5}(x^{2}-2x+1)
derivative of \sqrt[3]{x^2}+2sqrt(x^3)	\frac{d}{dx}(\sqrt[3]{x^{2}}+2\sqrt{x^{3}})
(\partial)/(\partial x)(5e^{yz}cos(xyz))	\frac{\partial\:}{\partial\:x}(5e^{yz}\cos(xyz))
area x^2-8x+15,0	area\:x^{2}-8x+15,0
derivative of 2xe^{-(x^2/2})	\frac{d}{dx}(2xe^{-\frac{x^{2}}{2}})
(\partial)/(\partial y)(yx)	\frac{\partial\:}{\partial\:y}(yx)
tangent of f(x)=6x^2-4x+4,(1,6)	tangent\:f(x)=6x^{2}-4x+4,(1,6)
(\partial)/(\partial y)(sqrt(4-x^2-8y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{4-x^{2}-8y^{2}})
derivative of y= 3/(e^x+e^{-x)}	derivative\:y=\frac{3}{e^{x}+e^{-x}}
derivative of 3x,-2y,x-y	\frac{d}{dx}(3x,-2y,x-y)
derivative of (e^{-x^2}(-2x))	\frac{d}{dx}((e^{-x^{2}})(-2x))
y^{''}+y=-sin(2x),y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y=-\sin(2x),y(0)=0,y^{\prime\:}(0)=0
integral of (ln(x^{20}))/x	\int\:\frac{\ln(x^{20})}{x}dx
integral of 1/((x^2+1)(x+1))	\int\:\frac{1}{(x^{2}+1)(x+1)}dx
integral of ((9+x+x^2))/(sqrt(x))	\int\:\frac{(9+x+x^{2})}{\sqrt{x}}dx
derivative of cos(2xsin(x))	\frac{d}{dx}(\cos(2x)\sin(x))
integral of t^5-7t	\int\:t^{5}-7tdt
(\partial)/(\partial x)(2x^2+4y^2+1)	\frac{\partial\:}{\partial\:x}(2x^{2}+4y^{2}+1)
derivative of 2^{x^3+3x}	\frac{d}{dx}(2^{x^{3}+3x})
tan(t)y^'-y=1	\tan(t)y^{\prime\:}-y=1
integral of x^2sqrt(x^2-9)	\int\:x^{2}\sqrt{x^{2}-9}dx
integral of (2x+3)/(2-x)	\int\:\frac{2x+3}{2-x}dx
integral of x(a^2-x^2)^{3/2}	\int\:x(a^{2}-x^{2})^{\frac{3}{2}}dx
integral of 1/(3x^212)	\int\:\frac{1}{3x^{2}12}dx
y^{''}+4y=10x(4-x),y(0)=-5,y(4)=10	y^{\prime\:\prime\:}+4y=10x(4-x),y(0)=-5,y(4)=10
derivative of x^2sinh(2x)	\frac{d}{dx}(x^{2}\sinh(2x))
integral from-pi to pi of e^xsin(nx)	\int\:_{-π}^{π}e^{x}\sin(nx)dx
integral of (sin(2x))/(49+cos^2(x))	\int\:\frac{\sin(2x)}{49+\cos^{2}(x)}dx
d/(dt)(t^3+3t)	\frac{d}{dt}(t^{3}+3t)

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