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Popular Calculus Problems

derivative of (sqrt(x))/(x+13)	derivative\:\frac{\sqrt{x}}{x+13}
limit as x approaches-5 of (x^2+6)/(x+2)	\lim\:_{x\to\:-5}(\frac{x^{2}+6}{x+2})
limit as x approaches 1 of x/(x^2-2x+1)	\lim\:_{x\to\:1}(\frac{x}{x^{2}-2x+1})
derivative of sqrt(6/5)*cos(x)	\frac{d}{dx}(\sqrt{\frac{6}{5}}\cdot\:\cos(x))
inverse oflaplace a/(2s^3)	inverselaplace\:\frac{a}{2s^{3}}
derivative of tan(xe^x)	derivative\:\tan(xe^{x})
limit as x approaches 0 of x^2+5x	\lim\:_{x\to\:0}(x^{2}+5x)
derivative of f(x)=sqrt(x^2+6x+1)	derivative\:f(x)=\sqrt{x^{2}+6x+1}
derivative of y=(x^2+e^x)sqrt(x)	derivative\:y=(x^{2}+e^{x})\sqrt{x}
d/(dy)(xsin(y))	\frac{d}{dy}(x\sin(y))
limit as x approaches infinity of 5/4	\lim\:_{x\to\:\infty\:}(\frac{5}{4})
derivative of Ine^x	\frac{d}{dx}(Ine^{x})
integral of (x^{17}+3e^x-cos(x)+1/x)	\int\:(x^{17}+3e^{x}-\cos(x)+\frac{1}{x})dx
derivative of f(x)=x^{-6}	derivative\:f(x)=x^{-6}
(\partial)/(\partial x)(1/(1-5/x))	\frac{\partial\:}{\partial\:x}(\frac{1}{1-\frac{5}{x}})
integral of (e^t+2t+ln(t))	\int\:(e^{t}+2t+\ln(t))dt
y^'=5y(1-y/7)	y^{\prime\:}=5y(1-\frac{y}{7})
d/(ds)(1)	\frac{d}{ds}(1)
derivative of (-2x-3^5(3x+1)^3)	\frac{d}{dx}((-2x-3)^{5}(3x+1)^{3})
sum from n=2 to infinity of ln(n)	\sum\:_{n=2}^{\infty\:}\ln(n)
limit as t approaches 0 of ln(t)	\lim\:_{t\to\:0}(\ln(t))
integral of cot(t)sqrt(sin^2(t)-25)	\int\:\cot(t)\sqrt{\sin^{2}(t)-25}dt
integral of 1-sin^2(x)	\int\:1-\sin^{2}(x)dx
derivative of (x-4^2)	\frac{d}{dx}((x-4)^{2})
derivative of ln(2x-sqrt(x))	\frac{d}{dx}(\ln(2x-\sqrt{x}))
integral of sqrt(x^3+x^2)(3x^2+2x)	\int\:\sqrt{x^{3}+x^{2}}(3x^{2}+2x)dx
integral of (5/x+(15)/(x^6))	\int\:(\frac{5}{x}+\frac{15}{x^{6}})dx
laplacetransform t-4	laplacetransform\:t-4
(x+y)y^'=2x+2*y-3	(x+y)\cdot\:y^{\prime\:}=2\cdot\:x+2\cdot\:y-3
integral of (e^{x-1})/x	\int\:\frac{e^{x-1}}{x}dx
derivative of 35x-xsqrt(x)	derivative\:35x-x\sqrt{x}
limit as x approaches 0 of sin(4x)	\lim\:_{x\to\:0}(\sin(4x))
integral of (x-1)/(x^2-4x-5)	\int\:\frac{x-1}{x^{2}-4x-5}dx
integral from 0 to 1 of sqrt(4t^2+9t^4)	\int\:_{0}^{1}\sqrt{4t^{2}+9t^{4}}dt
derivative of 1/x+x^2-2	\frac{d}{dx}(\frac{1}{x}+x^{2}-2)
derivative of (x^2+2x+1)/(x^2-2x+1)	derivative\:\frac{x^{2}+2x+1}{x^{2}-2x+1}
derivative of-7/(1+x^2)	derivative\:-\frac{7}{1+x^{2}}
sum from n=1 to infinity of n/(2n^3+3)	\sum\:_{n=1}^{\infty\:}\frac{n}{2n^{3}+3}
derivative of (4x+5)/(4x-5)	derivative\:\frac{4x+5}{4x-5}
inverse oflaplace 1/((s^2))	inverselaplace\:\frac{1}{(s^{2})}
integral of 1/(sqrt(x^2-4x+20))	\int\:\frac{1}{\sqrt{x^{2}-4x+20}}dx
f(x)=x^2sin(1/x)	f(x)=x^{2}\sin(\frac{1}{x})
(\partial)/(\partial x)(e^{x+y}sin(z)+(y+9)arccos(x))	\frac{\partial\:}{\partial\:x}(e^{x+y}\sin(z)+(y+9)\arccos(x))
laplacetransform (1+e^{4t})^2	laplacetransform\:(1+e^{4t})^{2}
integral of x^2sqrt(1+4x^2)	\int\:x^{2}\sqrt{1+4x^{2}}dx
integral of (xsqrt(6-x^2))	\int\:(x\sqrt{6-x^{2}})dx
derivative of cot(3x-3)	\frac{d}{dx}(\cot(3x-3))
(y^{''})/y =3	\frac{y^{\prime\:\prime\:}}{y}=3
(14-12y+e-3x)dx-4dy=0	(14-12y+e-3x)dx-4dy=0
sum from n=1 to infinity}(e^{1/n of)/n	\sum\:_{n=1}^{\infty\:}\frac{e^{\frac{1}{n}}}{n}
inverse oflaplace 1/((s+2)^2+4)	inverselaplace\:\frac{1}{(s+2)^{2}+4}
integral of (3x-4)/(x^2-x-2)	\int\:\frac{3x-4}{x^{2}-x-2}dx
integral of (5x^2+9x+5)/((x^2+1)^2)	\int\:\frac{5x^{2}+9x+5}{(x^{2}+1)^{2}}dx
d/(da)(sin(a)-sin(2a)+sin(3a))	\frac{d}{da}(\sin(a)-\sin(2a)+\sin(3a))
limit as x approaches 0-of xcot(x)	\lim\:_{x\to\:0-}(x\cot(x))
derivative of y= 7/(x^3)	derivative\:y=\frac{7}{x^{3}}
derivative of 1/(pi-x)	\frac{d}{dx}(\frac{1}{π-x})
(y^')/(y-y^2)= t/((1+t^2))	\frac{y^{\prime\:}}{y-y^{2}}=\frac{t}{(1+t^{2})}
tangent of f(x)=-2xcos(x),(pi,2pi)	tangent\:f(x)=-2x\cos(x),(π,2π)
sum from n=0 to infinity of n!2^n	\sum\:_{n=0}^{\infty\:}n!2^{n}
5sqrt(xy)((dy)/(dx))=4	5\sqrt{xy}(\frac{dy}{dx})=4
limit as x approaches 1 of ln(8x)+e^x	\lim\:_{x\to\:1}(\ln(8x)+e^{x})
derivative of 5e^{-0.5x}+100	\frac{d}{dx}(5e^{-0.5x}+100)
integral of (2^{18x})/4	\int\:\frac{2^{18x}}{4}dx
area y=4-x^2,y=16-7x	area\:y=4-x^{2},y=16-7x
(x^2+4)(dy)/(dx)=2x-8xy	(x^{2}+4)\frac{dy}{dx}=2x-8xy
limit as x approaches 2 of r(x)	\lim\:_{x\to\:2}(r(x))
(e^{x+y}+ye^y)dx+(xe^y-1)dy=0	(e^{x+y}+ye^{y})dx+(xe^{y}-1)dy=0
inverse oflaplace (s+1)/(s^2+2s+5)	inverselaplace\:\frac{s+1}{s^{2}+2s+5}
derivative of (x^2/(9-x^2))	\frac{d}{dx}(\frac{x^{2}}{9-x^{2}})
(\partial)/(\partial x)(2yx)	\frac{\partial\:}{\partial\:x}(2yx)
integral of (x^2)/(sqrt(x^2-x+1))	\int\:\frac{x^{2}}{\sqrt{x^{2}-x+1}}dx
derivative of f(x)=((x+1)(3x-7))/(3x+1)	derivative\:f(x)=\frac{(x+1)(3x-7)}{3x+1}
integral of x^4sqrt(9+x^5)	\int\:x^{4}\sqrt{9+x^{5}}dx
integral of 11x^{4/7}+4x^{-6/7}	\int\:11x^{\frac{4}{7}}+4x^{-\frac{6}{7}}dx
derivative of (ln(x)^{sinh(x)})	\frac{d}{dx}((\ln(x))^{\sinh(x)})
integral of 9cos(x)sin(x)	\int\:9\cos(x)\sin(x)dx
derivative of (x^2/7)	\frac{d}{dx}(\frac{x^{2}}{7})
tangent of f(x)=2x^3-4x^2,\at x=1	tangent\:f(x)=2x^{3}-4x^{2},\at\:x=1
integral from 1 to 5 of 5/(x^2+4x+4)	\int\:_{1}^{5}\frac{5}{x^{2}+4x+4}dx
derivative of x^2+2x-3	\frac{d}{dx}(x^{2}+2x-3)
(\partial)/(\partial y)((x^2)/(1+y^3))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}}{1+y^{3}})
derivative of axe^{bx^2}	\frac{d}{dx}(axe^{bx^{2}})
integral of-(arccot(x))/(1+x^2)	\int\:-\frac{\arccot(x)}{1+x^{2}}dx
(\partial)/(\partial x)(3x^2+6xy)	\frac{\partial\:}{\partial\:x}(3x^{2}+6xy)
derivative of (12(3x^3-16)/(4x-x^4))	\frac{d}{dx}(\frac{12(3x^{3}-16)}{4x-x^{4}})
integral of p(p+7)^8	\int\:p(p+7)^{8}dp
integral of t^2e^{-3t}	\int\:t^{2}e^{-3t}dt
integral of 2ye^{2x}	\int\:2ye^{2x}dx
y^{''}+2y^'+y=4e^{-1}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=4e^{-1}
d/(dt)(tan(t+pi/4))	\frac{d}{dt}(\tan(t+\frac{π}{4}))
(dy)/(dx)=y-y^5	\frac{dy}{dx}=y-y^{5}
(d^2y)/(dx^2)-2*(dy)/(dx)+ay=0,a>1	\frac{d^{2}y}{dx^{2}}-2\cdot\:\frac{dy}{dx}+ay=0,a>1
derivative of (x^5+1)/x	derivative\:\frac{x^{5}+1}{x}
integral from 0 to 1 of (8y)/(e^{2y)}	\int\:_{0}^{1}\frac{8y}{e^{2y}}dy
integral from 0 to 1 of 2pix(x^3-x^4)	\int\:_{0}^{1}2πx(x^{3}-x^{4})dx
integral of x/((x-3)^2)	\int\:\frac{x}{(x-3)^{2}}dx
(\partial)/(\partial x)((y^2)/(4-x^2))	\frac{\partial\:}{\partial\:x}(\frac{y^{2}}{4-x^{2}})
integral of 1/(-x^2+6x-10)	\int\:\frac{1}{-x^{2}+6x-10}dx
derivative of (sinh(x)^{2x^2+2x})	\frac{d}{dx}((\sinh(x))^{2x^{2}+2x})

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