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Popular Calculus Problems

integral of 1/(1+e^{ax)}	\int\:\frac{1}{1+e^{ax}}dx
integral of x/(x^4+16)	\int\:\frac{x}{x^{4}+16}dx
2y^{'''}-3y^{''}-18y^'-8y=0	2y^{\prime\:\prime\:\prime\:}-3y^{\prime\:\prime\:}-18y^{\prime\:}-8y=0
area y=3x^2-12,y=0	area\:y=3x^{2}-12,y=0
derivative of (3+sin(x)/(3x+cos(x)))	\frac{d}{dx}(\frac{3+\sin(x)}{3x+\cos(x)})
area y=e^x,y=e^{-3x},x=-2,x=1	area\:y=e^{x},y=e^{-3x},x=-2,x=1
derivative of e^{3(x-1})	\frac{d}{dx}(e^{3(x-1)})
integral of 3/(2+3x)	\int\:\frac{3}{2+3x}dx
limit as x approaches 4+of (x-2)/(x-4)	\lim\:_{x\to\:4+}(\frac{x-2}{x-4})
integral of 2xtan(x^2)	\int\:2x\tan(x^{2})dx
limit as x approaches-3 of (4x)/(x-3)	\lim\:_{x\to\:-3}(\frac{4x}{x-3})
integral of sin(9x)cos(2x)	\int\:\sin(9x)\cos(2x)dx
integral of 15cot^4(x)	\int\:15\cot^{4}(x)dx
(\partial)/(\partial x)(-2ycos^2(x))	\frac{\partial\:}{\partial\:x}(-2y\cos^{2}(x))
(dy)/(dx)+y=x^2+1	\frac{dy}{dx}+y=x^{2}+1
(\partial)/(\partial x)(y^2-cos(xy))	\frac{\partial\:}{\partial\:x}(y^{2}-\cos(xy))
(dy)/(dx)y=(3x-2x^2)^3	\frac{dy}{dx}y=(3x-2x^{2})^{3}
derivative of f(x)=(x^2)/((3+x))	derivative\:f(x)=\frac{x^{2}}{(3+x)}
taylor e^{1/6 x^6},0	taylor\:e^{\frac{1}{6}x^{6}},0
limit as x approaches-6-of-1/(x+6)	\lim\:_{x\to\:-6-}(-\frac{1}{x+6})
integral from 1 to 3 of (3-x)^2	\int\:_{1}^{3}(3-x)^{2}dx
derivative of 1/(e^x+e^{-x})	\frac{d}{dx}(\frac{1}{e^{x}+e^{-x}})
integral of (x+1)/(e^x)	\int\:\frac{x+1}{e^{x}}dx
derivative of (x-1/(x^2-x+1))	\frac{d}{dx}(\frac{x-1}{x^{2}-x+1})
integral of x/(-x-1)	\int\:\frac{x}{-x-1}dx
integral of 4x^3+2xy^2ln(x^2+y^2)	\int\:4x^{3}+2xy^{2}\ln(x^{2}+y^{2})dx
(x^2-xy)dx+xdy=0	(x^{2}-xy)dx+xdy=0
integral of (x^3+2)/(x^2+8x+7)	\int\:\frac{x^{3}+2}{x^{2}+8x+7}dx
integral of (x+1)/(x-2)	\int\:\frac{x+1}{x-2}dx
sum from n=0 to infinity of 7/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{7}{5^{n}}
integral of-7sec(2x)tan(2x)	\int\:-7\sec(2x)\tan(2x)dx
integral of (3x)/(x^2+1)	\int\:\frac{3x}{x^{2}+1}dx
integral of (2x-3)/(x^2-3x+2)	\int\:\frac{2x-3}{x^{2}-3x+2}dx
derivative of e^{3x-2}	\frac{d}{dx}(e^{3x-2})
integral of cot^3(5x)	\int\:\cot^{3}(5x)dx
derivative of f(x)=8xsin(pix)	derivative\:f(x)=8x\sin(πx)
derivative of 4t^{-1/8}+4ln(t)+ln(5)	derivative\:4t^{-\frac{1}{8}}+4\ln(t)+\ln(5)
integral of (x^2+3x+2)e^x	\int\:(x^{2}+3x+2)e^{x}dx
limit as x approaches 3 of 4x^2-1/x	\lim\:_{x\to\:3}(4x^{2}-\frac{1}{x})
integral of (2x^3+7x^2+2x+9)/(2x+3)	\int\:\frac{2x^{3}+7x^{2}+2x+9}{2x+3}dx
derivative of xe^{-x^{10}}	derivative\:xe^{-x^{10}}
y^'-2y=-4y^3	y^{\prime\:}-2y=-4y^{3}
integral of x^3e^2	\int\:x^{3}e^{2}dx
integral of (1+t)^2	\int\:(1+t)^{2}dt
tangent of 2/(sqrt(x+5)),\at x=4	tangent\:\frac{2}{\sqrt{x+5}},\at\:x=4
tangent of f(x)=2x^2-x-3,\at x=1	tangent\:f(x)=2x^{2}-x-3,\at\:x=1
derivative of y=sqrt(2-6x)	derivative\:y=\sqrt{2-6x}
derivative of y=(2x+4)/(1-x)	derivative\:y=\frac{2x+4}{1-x}
3y^{''}+2y^'=0	3y^{\prime\:\prime\:}+2y^{\prime\:}=0
(dN)/(dt)+N=Nte^{t+4}	\frac{dN}{dt}+N=Nte^{t+4}
integral of x+11	\int\:x+11dx
integral of x/(sqrt(6x^2+5))	\int\:\frac{x}{\sqrt{6x^{2}+5}}dx
derivative of f(x)=x^4e^{2x}	derivative\:f(x)=x^{4}e^{2x}
derivative of 4x+(16)/(x^2)	derivative\:4x+\frac{16}{x^{2}}
integral from 0 to 1 of x^2e^{x^3}	\int\:_{0}^{1}x^{2}e^{x^{3}}dx
(dy)/(dx)=-0.5y+x	\frac{dy}{dx}=-0.5y+x
integral of sqrt(x/3)	\int\:\sqrt{\frac{x}{3}}dx
y^{''}+3y=-9	y^{\prime\:\prime\:}+3y=-9
derivative of-2cot(x)csc(x)	derivative\:-2\cot(x)\csc(x)
limit as x approaches 2pi of 1/(sin(x))	\lim\:_{x\to\:2π}(\frac{1}{\sin(x)})
maclaurin sin(2x)	maclaurin\:\sin(2x)
derivative of (x^4-4x+3/(sqrt(x)+1))	\frac{d}{dx}(\frac{x^{4}-4x+3}{\sqrt{x}+1})
(sqrt(y))^'	(\sqrt{y})^{\prime\:}
integral from x to x^2 of t^2	\int\:_{x}^{x^{2}}t^{2}dt
(dy)/(dx)7x+y=x-6x	\frac{dy}{dx}7x+y=x-6x
integral of (e^x)/(1+e^{2x)}	\int\:\frac{e^{x}}{1+e^{2x}}dx
(\partial)/(\partial x)(x/(y+z))	\frac{\partial\:}{\partial\:x}(\frac{x}{y+z})
integral of xsin(4x^2)	\int\:x\sin(4x^{2})dx
limit as x approaches-2 of 4-2x	\lim\:_{x\to\:-2}(4-2x)
(\partial)/(\partial x)((3x-x^2)ye^{-y})	\frac{\partial\:}{\partial\:x}((3x-x^{2})ye^{-y})
limit as x approaches 0 of x^2cos(7/x)	\lim\:_{x\to\:0}(x^{2}\cos(\frac{7}{x}))
(4e^x)^'	(4e^{x})^{\prime\:}
derivative of (7x)/(e^x)	derivative\:\frac{7x}{e^{x}}
derivative of 8^{-3x^2}	\frac{d}{dx}(8^{-3x^{2}})
integral of 3/(\sqrt[4]{2x+5)}	\int\:\frac{3}{\sqrt[4]{2x+5}}dx
limit as x approaches 5+of-ln(5-x)	\lim\:_{x\to\:5+}(-\ln(5-x))
laplacetransform e^{-2t}sin(3t)	laplacetransform\:e^{-2t}\sin(3t)
(\partial)/(\partial x)(x^3+3xy^2)	\frac{\partial\:}{\partial\:x}(x^{3}+3xy^{2})
slope of (7,3),(2,-3)	slope\:(7,3),(2,-3)
area 4x-x^2,x	area\:4x-x^{2},x
derivative of f(x)=ln(ln(x^2))	derivative\:f(x)=\ln(\ln(x^{2}))
limit as x approaches 1 of \|2x\|	\lim\:_{x\to\:1}(\left\|2x\right\|)
implicit (dy)/(dx),x+y^2=1	implicit\:\frac{dy}{dx},x+y^{2}=1
limit as x approaches 0-of 3	\lim\:_{x\to\:0-}(3)
d/(dθ)(8cos(θ)-6sin(θ))	\frac{d}{dθ}(8\cos(θ)-6\sin(θ))
derivative of f(x)=((-2))/x	derivative\:f(x)=\frac{(-2)}{x}
derivative of 4x^4+3x^2	\frac{d}{dx}(4x^{4}+3x^{2})
derivative of f(x)=5+x^2	derivative\:f(x)=5+x^{2}
integral from 0 to 1/2 of t^2	\int\:_{0}^{\frac{1}{2}}t^{2}dt
(\partial)/(\partial x)(8+e^{-xy}cos(y))	\frac{\partial\:}{\partial\:x}(8+e^{-xy}\cos(y))
tangent of f(x)= 1/(2+3x),(2, 1/8)	tangent\:f(x)=\frac{1}{2+3x},(2,\frac{1}{8})
derivative of y=sqrt(1-2x)	derivative\:y=\sqrt{1-2x}
derivative of g(x)=(x^2+1)^3(x^2+2)^6	derivative\:g(x)=(x^{2}+1)^{3}(x^{2}+2)^{6}
inverse oflaplace (s+3)/(s^2+2s+1)	inverselaplace\:\frac{s+3}{s^{2}+2s+1}
derivative of f(x)=4x^4-1/(4x^4)	derivative\:f(x)=4x^{4}-\frac{1}{4x^{4}}
y^{''}+2y^'+y=-e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=-e^{-t}
(\partial)/(\partial y)((x^3)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{x^{3}}{x^{2}+y^{2}})
sum from n=1 to infinity of (-5x)^n	\sum\:_{n=1}^{\infty\:}(-5x)^{n}
integral of (x+4)(2x+1)	\int\:(x+4)(2x+1)dx
(d^2)/(dx^2)(2x^2)	\frac{d^{2}}{dx^{2}}(2x^{2})

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