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Popular Calculus Problems

integral of (1-cos(x))	\int\:(1-\cos(x))dx
integral of 1/(e^{2x)+1}	\int\:\frac{1}{e^{2x}+1}dx
integral of sqrt((4-x)x)	\int\:\sqrt{(4-x)x}dx
y^'+3y=t+e^{(-2t)}	y^{\prime\:}+3y=t+e^{(-2t)}
limit as x approaches-3 of 1/((x+3)^2)	\lim\:_{x\to\:-3}(\frac{1}{(x+3)^{2}})
y^'-e^xe^y=-1	y^{\prime\:}-e^{x}e^{y}=-1
(\partial)/(\partial x)(e^{1+x^2-y^2})	\frac{\partial\:}{\partial\:x}(e^{1+x^{2}-y^{2}})
derivative of 6cos(2x-e^{-x})	\frac{d}{dx}(6\cos(2x)-e^{-x})
tangent of f(x)=2x^3+7x^2-8x-3,\at x=-1	tangent\:f(x)=2x^{3}+7x^{2}-8x-3,\at\:x=-1
limit as x approaches 1-of 1-x-[x]-[1-x]	\lim\:_{x\to\:1-}(1-x-[x]-[1-x])
limit as x approaches 4-of 1/((x-4)^2)	\lim\:_{x\to\:4-}(\frac{1}{(x-4)^{2}})
derivative of f(x)=x^{(7)}-3e^{(3x)}	derivative\:f(x)=x^{(7)}-3e^{(3x)}
limit as x approaches 0 of (1+4x)^{1/x}	\lim\:_{x\to\:0}((1+4x)^{\frac{1}{x}})
2y^{''}+3y^'-2y=25e^{-2x}	2y^{\prime\:\prime\:}+3y^{\prime\:}-2y=25e^{-2x}
slope ofintercept (-2,-1),(2,4)	slopeintercept\:(-2,-1),(2,4)
integral of 8x*csc^2(4x)	\int\:8x\cdot\:\csc^{2}(4x)dx
integral of 2^{5x+2}	\int\:2^{5x+2}dx
2xy^'+y=6x,y(4)=15	2xy^{\prime\:}+y=6x,y(4)=15
derivative of \sqrt[3]{2x-7}	\frac{d}{dx}(\sqrt[3]{2x-7})
integral of (x')/(x^2)	\int\:\frac{x\prime\:}{x^{2}}dx
(\partial)/(\partial x)(2xy-3xz^2)	\frac{\partial\:}{\partial\:x}(2xy-3xz^{2})
integral of 5sin^4(xco)s^2x	\int\:5\sin^{4}(xco)s^{2}xdx
derivative of (x^2+2x/(3x+6))	\frac{d}{dx}(\frac{x^{2}+2x}{3x+6})
limit as x approaches-1 of x^3-2	\lim\:_{x\to\:-1}(x^{3}-2)
parity cot^2(sin(θ))	parity\:\cot^{2}(\sin(θ))
limit as x approaches 0 of (x^2+x)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{2}+x}{x^{2}})
laplacetransform-6t^2	laplacetransform\:-6t^{2}
(\partial)/(\partial x)(sqrt(xy)-xy)	\frac{\partial\:}{\partial\:x}(\sqrt{x\cdot\:y}-x\cdot\:y)
derivative of cos(x^2+1)	\frac{d}{dx}(\cos(x^{2}+1))
integral of x/(sqrt(x^2+6))	\int\:\frac{x}{\sqrt{x^{2}+6}}dx
integral of 10x^2	\int\:10x^{2}dx
integral of e^{7x}sin(5x)	\int\:e^{7x}\sin(5x)dx
(dy)/(dx)=-(y^2)/(1+y^2)*e^{-x}	\frac{dy}{dx}=-\frac{y^{2}}{1+y^{2}}\cdot\:e^{-x}
integral of x(2x+5)^{10}	\int\:x(2x+5)^{10}dx
integral of ln(x)x^3	\int\:\ln(x)x^{3}dx
integral of x(-cos(x+pi/3)+cos(x))	\int\:x(-\cos(x+\frac{π}{3})+\cos(x))dx
factor x^5+2x^4-11x^3-12x^2+36x	factor\:x^{5}+2x^{4}-11x^{3}-12x^{2}+36x
derivative of-1/(x^2-7/x)	\frac{d}{dx}(-\frac{1}{x^{2}}-\frac{7}{x})
area 4-x^2,-x+2	area\:4-x^{2},-x+2
derivative of e^2X	derivative\:e^{2}X
(dy)/(dx)=x(1+y^2)	\frac{dy}{dx}=x(1+y^{2})
(\partial)/(\partial x)(sin(x)cos(y))	\frac{\partial\:}{\partial\:x}(\sin(x)\cos(y))
(\partial)/(\partial y)(cos(x^2+xy))	\frac{\partial\:}{\partial\:y}(\cos(x^{2}+xy))
integral of a^u	\int\:a^{u}du
derivative of 3/(t^2)	derivative\:\frac{3}{t^{2}}
integral of cos^3(θ)	\int\:\cos^{3}(θ)dθ
(\partial)/(\partial x)(((x+y))/(x-y))	\frac{\partial\:}{\partial\:x}(\frac{(x+y)}{x-y})
integral from 0 to 1 of sqrt(1+x^4+2x^2)	\int\:_{0}^{1}\sqrt{1+x^{4}+2x^{2}}dx
integral of 1/((x+1)(x-2))	\int\:\frac{1}{(x+1)(x-2)}dx
integral from 6 to 8 of ((x^2+6)/(x^2))	\int\:_{6}^{8}(\frac{x^{2}+6}{x^{2}})dx
integral of (x^3-x^2+x-1)/(x^2+9)	\int\:\frac{x^{3}-x^{2}+x-1}{x^{2}+9}dx
derivative of (x+1)/(x^2)	derivative\:\frac{x+1}{x^{2}}
limit as x approaches 2 of log_{4}(x-2)	\lim\:_{x\to\:2}(\log_{4}(x-2))
(dy)/(dx)+3x^2y=x^2	\frac{dy}{dx}+3x^{2}y=x^{2}
(dy)/(dx)=10xe^{5y}	\frac{dy}{dx}=10xe^{5y}
derivative of f(x)= 2/(sqrt(x))	derivative\:f(x)=\frac{2}{\sqrt{x}}
derivative of sin^3(4x^2-1)	\frac{d}{dx}(\sin^{3}(4x^{2}-1))
limit as x approaches pi/2 of ln(sin(x))	\lim\:_{x\to\:\frac{π}{2}}(\ln(\sin(x)))
area 2/x ,8x, 1/2 x	area\:\frac{2}{x},8x,\frac{1}{2}x
limit as x approaches 3 of 2-x	\lim\:_{x\to\:3}(2-x)
derivative of (1-cos(x)/(1+sin(x)))	\frac{d}{dx}(\frac{1-\cos(x)}{1+\sin(x)})
derivative of-(e^{x-1}(x-3)/((x-1)^3))	\frac{d}{dx}(-\frac{e^{x-1}(x-3)}{(x-1)^{3}})
inverse oflaplace e^s 1/(s^2)	inverselaplace\:e^{s}\frac{1}{s^{2}}
limit as x approaches 1 of (x^2+x)/(x+1)	\lim\:_{x\to\:1}(\frac{x^{2}+x}{x+1})
derivative of (2x+1/(x+3))	\frac{d}{dx}(\frac{2x+1}{x+3})
(dy)/(dt)=ty+t	\frac{dy}{dt}=ty+t
(dy)/(dx)= 1/2 x+4	\frac{dy}{dx}=\frac{1}{2}x+4
(dy)/(dx)+xy= x/(y^3)	\frac{dy}{dx}+xy=\frac{x}{y^{3}}
integral of 7/(x^2-6x+25)	\int\:\frac{7}{x^{2}-6x+25}dx
area x^2+2x,1,2	area\:x^{2}+2x,1,2
integral from-2 to 2 of (16)/(x^2-4x-60)	\int\:_{-2}^{2}\frac{16}{x^{2}-4x-60}dx
y^{'''}+y^'=x	y^{\prime\:\prime\:\prime\:}+y^{\prime\:}=x
derivative of (x-1e^x)	\frac{d}{dx}((x-1)e^{x})
inverse oflaplace 7/(s^2+42)	inverselaplace\:\frac{7}{s^{2}+42}
(\partial)/(\partial x)(x^2-7xy+y)	\frac{\partial\:}{\partial\:x}(x^{2}-7xy+y)
integral of csc^2(x/5)	\int\:\csc^{2}(\frac{x}{5})dx
(\partial)/(\partial x)(sin(x^2-7xy))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}-7xy))
integral from 0 to infinity of e^{-x}x	\int\:_{0}^{\infty\:}e^{-x}xdx
(\partial)/(\partial z)(sin(x))	\frac{\partial\:}{\partial\:z}(\sin(x))
(\partial)/(\partial x)(e^{-8y}sin(8x))	\frac{\partial\:}{\partial\:x}(e^{-8y}\sin(8x))
derivative of {f}(x(x{f}(x)(x{f}(x))))	\frac{d}{dx}({f}(x)(x{f}(x)(x{f}(x))))
derivative of 3^{xln(x})	\frac{d}{dx}(3^{x\ln(x)})
derivative of log_{e}(sin(2x)+cot(2x))	derivative\:\log_{e}(\sin(2x)+\cot(2x))
derivative of y= 1/2 x	derivative\:y=\frac{1}{2}x
integral from pi to 2pi of (t-pi)e^{-st}	\int\:_{π}^{2π}(t-π)e^{-st}dt
derivative of 13-x^2	derivative\:13-x^{2}
(\partial)/(\partial y)(3arctan(x/y))	\frac{\partial\:}{\partial\:y}(3\arctan(\frac{x}{y}))
(\partial)/(\partial y)(-sin(xy)y)	\frac{\partial\:}{\partial\:y}(-\sin(xy)y)
integral of (1-2x)^{3/2}	\int\:(1-2x)^{\frac{3}{2}}dx
limit as x approaches 0 of sqrt(x^2-x^4)	\lim\:_{x\to\:0}(\sqrt{x^{2}-x^{4}})
(\partial)/(\partial x)(6xy-2+10x^2y^2)	\frac{\partial\:}{\partial\:x}(6xy-2+10x^{2}y^{2})
(\partial)/(\partial x)(xarctan(y+z))	\frac{\partial\:}{\partial\:x}(x\arctan(y+z))
tangent of f(x)= x/(-6x+6),\at x=2	tangent\:f(x)=\frac{x}{-6x+6},\at\:x=2
derivative of (x^2-3x+1/(sqrt(x)))	\frac{d}{dx}(\frac{x^{2}-3x+1}{\sqrt{x}})
limit as x approaches 5 of 1/((x-5)^2)	\lim\:_{x\to\:5}(\frac{1}{(x-5)^{2}})
integral of (x^2)/(2sqrt(1-x^2))	\int\:\frac{x^{2}}{2\sqrt{1-x^{2}}}dx
derivative of x/(2pi)	\frac{d}{dx}(\frac{x}{2π})
integral of b/(sqrt(b^2-2b+2))	\int\:\frac{b}{\sqrt{b^{2}-2b+2}}
integral of 3x^2(x^3+8)^5	\int\:3x^{2}(x^{3}+8)^{5}dx
derivative of y=-2sin(x^2)	derivative\:y=-2\sin(x^{2})

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