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Popular Calculus Problems

area y=10x,y=x^2-11	area\:y=10x,y=x^{2}-11
integral of x(2x+1)	\int\:x(2x+1)dx
(\partial)/(\partial y)(msin(2(mx+ny)))	\frac{\partial\:}{\partial\:y}(m\sin(2(mx+ny)))
tangent of y= 1/(3t),(2, 1/6)	tangent\:y=\frac{1}{3t},(2,\frac{1}{6})
integral of x*cos^2(x)	\int\:x\cdot\:\cos^{2}(x)dx
maclaurin g(x)= x/(x-1)	maclaurin\:g(x)=\frac{x}{x-1}
f^{''}(x)= 6/x	f^{\prime\:\prime\:}(x)=\frac{6}{x}
limit as x approaches 0 of 1-2sin^2(x/2)	\lim\:_{x\to\:0}(1-2\sin^{2}(\frac{x}{2}))
limit as x approaches 1+of sqrt(2x-2)-2	\lim\:_{x\to\:1+}(\sqrt{2x-2}-2)
integral of (6x+5)/(sqrt(3x^2+5x))	\int\:\frac{6x+5}{\sqrt{3x^{2}+5x}}dx
integral from 3 to 5 of 1/(sqrt(x^2-9))	\int\:_{3}^{5}\frac{1}{\sqrt{x^{2}-9}}dx
derivative of f(x)=(x^3-10x)(3x^2+4x)	derivative\:f(x)=(x^{3}-10x)(3x^{2}+4x)
area y=x^2ln(x),y=4ln(x)	area\:y=x^{2}\ln(x),y=4\ln(x)
derivative of (e^{2x}\sqrt[3]{x^3+1})	\frac{d}{dx}((e^{2x})\sqrt[3]{x^{3}+1})
derivative of e^{(x+2/(x-2)})	\frac{d}{dx}(e^{\frac{x+2}{x-2}})
integral from-8 to 8 of (4x^9+7x^5)	\int\:_{-8}^{8}(4x^{9}+7x^{5})dx
tangent of y=((x+5)^5)/(7x-5)	tangent\:y=\frac{(x+5)^{5}}{7x-5}
integral from 0 to 6 of 2pix(6x-x^2)	\int\:_{0}^{6}2πx(6x-x^{2})dx
derivative of cos^2(x-cos(x))	\frac{d}{dx}(\cos^{2}(x)-\cos(x))
derivative of m(m-1x^{m-2})	\frac{d}{dx}(m(m-1)x^{m-2})
derivative of arctan(1)	\frac{d}{dx}(\arctan(1))
integral of (1-x^{3/2})^{5/3}*sqrt(x)	\int\:(1-x^{\frac{3}{2}})^{\frac{5}{3}}\cdot\:\sqrt{x}dx
derivative of sin((5x^2+8^8))	\frac{d}{dx}(\sin((5x^{2}+8)^{8}))
limit as x approaches infinity of 5x-1	\lim\:_{x\to\:\infty\:}(5x-1)
derivative of sqrt(2t^2-t)	derivative\:\sqrt{2t^{2}-t}
derivative of x-inx	\frac{d}{dx}(x-inx)
laplacetransform te^{-0.003t}cos(10t)	laplacetransform\:te^{-0.003t}\cos(10t)
integral from 0 to 1 of 1/((x+1)(x^2+1))	\int\:_{0}^{1}\frac{1}{(x+1)(x^{2}+1)}dx
tangent of f(x)=x^4+8x^3+2x+2,\at x=1	tangent\:f(x)=x^{4}+8x^{3}+2x+2,\at\:x=1
(\partial)/(\partial x)((12x)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{12x}{x+y})
derivative of f(x)=(-x^3+x^2+x)cos(x)	derivative\:f(x)=(-x^{3}+x^{2}+x)\cos(x)
integral of x^2-2x+1	\int\:x^{2}-2x+1dx
integral of x^{2k}	\int\:x^{2k}dx
integral of 1/(x+6)	\int\:\frac{1}{x+6}dx
(\partial)/(\partial x)(x^{-2})	\frac{\partial\:}{\partial\:x}(x^{-2})
integral of x^{-0.9}	\int\:x^{-0.9}dx
taylor (1-x)e^{x+(x^2)/2+(x^3)/3}	taylor\:(1-x)e^{x+\frac{x^{2}}{2}+\frac{x^{3}}{3}}
integral of sin(ln(u))	\int\:\sin(\ln(u))du
y^{''}-y=5sin(2t)(0)1	y^{\prime\:\prime\:}-y=5\sin(2t)(0)1
taylor 1/(2+3x)	taylor\:\frac{1}{2+3x}
y^'=y+x,y(0)=-1	y^{\prime\:}=y+x,y(0)=-1
derivative of r/(sqrt(r^2+1))	derivative\:\frac{r}{\sqrt{r^{2}+1}}
integral of (-0.5x+450)	\int\:(-0.5x+450)dx
(dy)/(dx)=4x-5	\frac{dy}{dx}=4x-5
limit as x approaches 0 of (x)^{tan(x)}	\lim\:_{x\to\:0}((x)^{\tan(x)})
(\partial)/(\partial x)(y/(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{x^{2}+y^{2}+z^{2}})
slope of y=sqrt(7x+1),(5,6)	slope\:y=\sqrt{7x+1},(5,6)
(\partial)/(\partial x)(xye^{x-2z})	\frac{\partial\:}{\partial\:x}(xye^{x-2z})
(\partial)/(\partial x)(A+B*cos(x)sin(y))	\frac{\partial\:}{\partial\:x}(A+B\cdot\:\cos(x)\sin(y))
(dx)/(dt)=x^{2/3}	\frac{dx}{dt}=x^{\frac{2}{3}}
inverse oflaplace 1/(4s^2)	inverselaplace\:\frac{1}{4s^{2}}
y^'-y=3te^{2t},y(0)=1	y^{\prime\:}-y=3te^{2t},y(0)=1
derivative of 2sin(t)	derivative\:2\sin(t)
(\partial)/(\partial x)(ye^{(x/y)})	\frac{\partial\:}{\partial\:x}(ye^{(\frac{x}{y})})
(d^2)/(dx^2)((x^2-4x)/(x+1))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}-4x}{x+1})
derivative of 3x^2sqrt(5x+3)	\frac{d}{dx}(3x^{2}\sqrt{5x+3})
tangent of f(x)=sqrt(2-10x),\at x=-1	tangent\:f(x)=\sqrt{2-10x},\at\:x=-1
integral of (7x)	\int\:(7x)dx
derivative of \sqrt[3]{sin(x})	\frac{d}{dx}(\sqrt[3]{\sin(x)})
integral of 1/(1+u^2)	\int\:\frac{1}{1+u^{2}}du
integral of (x^3)/((1+x^4))	\int\:\frac{x^{3}}{(1+x^{4})}dx
limit as x approaches 0 of x^2+x-3	\lim\:_{x\to\:0}(x^{2}+x-3)
integral from 0 to 1 of 2piy(y-y^2)	\int\:_{0}^{1}2πy(y-y^{2})dy
(\partial)/(\partial x)(sin(pixy))	\frac{\partial\:}{\partial\:x}(\sin(pixy))
integral of (2+5x^4)x^3	\int\:(2+5x^{4})x^{3}dx
integral of 1/(xsqrt(400x^2-400))	\int\:\frac{1}{x\sqrt{400x^{2}-400}}dx
integral of 1/(x^3-8)	\int\:\frac{1}{x^{3}-8}dx
derivative of f(x)=(7x^2-11x)e^x	derivative\:f(x)=(7x^{2}-11x)e^{x}
(\partial)/(\partial z)(x-z-arctan(yz))	\frac{\partial\:}{\partial\:z}(x-z-\arctan(yz))
integral of 6xsec(x)tan(x)	\int\:6x\sec(x)\tan(x)dx
derivative of 60x^4-180x^3+180x^2-60x	\frac{d}{dx}(60x^{4}-180x^{3}+180x^{2}-60x)
derivative of ln(x^2+10)	\frac{d}{dx}(\ln(x^{2}+10))
d/(dt)(10000(12+t)e^{-0.05t})	\frac{d}{dt}(10000(12+t)e^{-0.05t})
integral of 5/((3x-1))	\int\:\frac{5}{(3x-1)}dx
derivative of e^{60x+50x^2}	\frac{d}{dx}(e^{60x+50x^{2}})
(dy)/(dx)=(y^3-x^3)/(xy^2)	\frac{dy}{dx}=\frac{y^{3}-x^{3}}{xy^{2}}
derivative of 2log_{5}(x)	derivative\:2\log_{5}(x)
limit as x approaches 6 of (10)(-5)	\lim\:_{x\to\:6}((10)(-5))
integral of 1/(sqrt(3))	\int\:\frac{1}{\sqrt{3}}
integral of 1/2 x^{-2}	\int\:\frac{1}{2}x^{-2}dx
derivative of 8cos(4x)	derivative\:8\cos(4x)
integral of a^{nx}	\int\:a^{nx}dx
derivative of e^{x+6}	\frac{d}{dx}(e^{x+6})
f(x)=ln(x^2+5)	f(x)=\ln(x^{2}+5)
y^{''}-36y=e^{6x}	y^{\prime\:\prime\:}-36y=e^{6x}
derivative of tan(x^2+tan^2(x))	\frac{d}{dx}(\tan(x^{2})+\tan^{2}(x))
y^'-2y=e^{3t}	y^{\prime\:}-2y=e^{3t}
derivative of-6/x	derivative\:-\frac{6}{x}
sum from n=0 to infinity of ((-1)x^n)/n	\sum\:_{n=0}^{\infty\:}\frac{(-1)x^{n}}{n}
(\partial)/(\partial v)(v/2)	\frac{\partial\:}{\partial\:v}(\frac{v}{2})
2sin(2x)dx+3e^{3y}dy=2xdx	2\sin(2x)dx+3e^{3y}dy=2xdx
integral from-2 to-1 of x^2-x-2	\int\:_{-2}^{-1}x^{2}-x-2dx
(dy)/(dx)=(3x+2y)/(3x+2y+2)	\frac{dy}{dx}=\frac{3x+2y}{3x+2y+2}
y^{''}+7y^'+10y=-4sin(3t)	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=-4\sin(3t)
derivative of sin^2(3x)	derivative\:\sin^{2}(3x)
tangent of f(x)=(6x-2)^{1/4},\at x=1	tangent\:f(x)=(6x-2)^{\frac{1}{4}},\at\:x=1
derivative of 8/t	derivative\:\frac{8}{t}
integral of xsin(x)cos(x)	\int\:x\sin(x)\cos(x)dx
derivative of (2-x^2)	\frac{d}{dx}((2-x)^{2})
(\partial)/(\partial x)(4xy-10x^2y^2z+5z^2)	\frac{\partial\:}{\partial\:x}(4xy-10x^{2}y^{2}z+5z^{2})

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