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Popular Calculus Problems

integral of (e^{x-1+ln(x-1)})/(e^{2x)}	\int\:\frac{e^{x-1+\ln(x-1)}}{e^{2x}}dx
integral of ((15)/(x^2+1))	\int\:(\frac{15}{x^{2}+1})dx
integral of (5x^2-8x)e^{2x}	\int\:(5x^{2}-8x)e^{2x}dx
integral from 0 to 1 of (13)/(x^5)	\int\:_{0}^{1}\frac{13}{x^{5}}dx
derivative of 2x^2	derivative\:2x^{2}
derivative of f(x)= 3/5 x^{10}	derivative\:f(x)=\frac{3}{5}x^{10}
derivative of (sqrt((x^2-4^3))/6)	\frac{d}{dx}(\frac{\sqrt{(x^{2}-4)^{3}}}{6})
integral of 1/(y(y+1))	\int\:\frac{1}{y(y+1)}dy
y^'=2ty(1-y)	y^{\prime\:}=2ty(1-y)
area x,0,0.085	area\:x,0,0.085
(dy)/(dx)+2y=e^{3x}	\frac{dy}{dx}+2y=e^{3x}
derivative of 5sin(3x)	\frac{d}{dx}(5\sin(3x))
derivative of x^8e^{6x}	derivative\:x^{8}e^{6x}
(2x^3)^'	(2x^{3})^{\prime\:}
derivative of (x-1)/(x^3)	derivative\:\frac{x-1}{x^{3}}
integral of (x^2-3)^2	\int\:(x^{2}-3)^{2}dx
derivative of 6sqrt(8x^2+9)	derivative\:6\sqrt{8x^{2}+9}
derivative of (2x-1/(x+3))	\frac{d}{dx}(\frac{2x-1}{x+3})
limit as x approaches 3 of-2	\lim\:_{x\to\:3}(-2)
integral of-8xe^{x^2}	\int\:-8xe^{x^{2}}dx
integral of sin^5(x)cos^3(x)	\int\:\sin^{5}(x)\cos^{3}(x)dx
integral of+e^{8x}cos(3x)	\int\:+e^{8x}\cos(3x)dx
derivative of (e^x+e^{-x}/7)	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{7})
inverse oflaplace (3(s+1)*e^{-2s})/(s(s+1)(2s+1))	inverselaplace\:\frac{3(s+1)\cdot\:e^{-2s}}{s(s+1)(2s+1)}
derivative of (2x+1)/(2x-1)	derivative\:\frac{2x+1}{2x-1}
integral of t-2	\int\:t-2dt
integral of 1/((x^2+r^2)^{3/2)}	\int\:\frac{1}{(x^{2}+r^{2})^{\frac{3}{2}}}dx
inverse oflaplace (e^{-3s})/(s+3)	inverselaplace\:\frac{e^{-3s}}{s+3}
integral of x-csc(x)*cotan(x)	\int\:x-\csc(x)\cdot\:co\tan(x)
integral of arcsin(1)	\int\:\arcsin(1)dx
derivative of f(x)=-x^3	derivative\:f(x)=-x^{3}
derivative of (-1/(2x^{3/2)})	\frac{d}{dx}(\frac{-1}{2x^{\frac{3}{2}}})
derivative of sqrt(sec(x^3))	\frac{d}{dx}(\sqrt{\sec(x^{3})})
derivative of arcsin(1/(sqrt(1+x^2)))	\frac{d}{dx}(\arcsin(\frac{1}{\sqrt{1+x^{2}}}))
integral from 4 to infinity of xe^{-2x}	\int\:_{4}^{\infty\:}xe^{-2x}dx
integral from-3 to 5 of 2y-(y^2-15)	\int\:_{-3}^{5}2y-(y^{2}-15)dy
(\partial)/(\partial x)(3xarctan(x/y))	\frac{\partial\:}{\partial\:x}(3x\arctan(\frac{x}{y}))
derivative of 4e^x+x	derivative\:4e^{x}+x
(dy}{dx}=-\frac{2x)/y	\frac{dy}{dx}=-\frac{2x}{y}
tangent of (x+1)(4x^2-4x-8)	tangent\:(x+1)(4x^{2}-4x-8)
(\partial)/(\partial x)(x^3y-xy^3)	\frac{\partial\:}{\partial\:x}(x^{3}y-xy^{3})
(-12xy^2-12y)+(-12x^2y-12x)y^'=0	(-12xy^{2}-12y)+(-12x^{2}y-12x)y^{\prime\:}=0
integral of e^{-4x}	\int\:e^{-4x}dx
integral of ((x^{10}))/(x^2+x-2)	\int\:\frac{(x^{10})}{x^{2}+x-2}dx
tangent of f(x)= 4/x ,\at x=3	tangent\:f(x)=\frac{4}{x},\at\:x=3
inverse oflaplace 1/(4s^2+1)	inverselaplace\:\frac{1}{4s^{2}+1}
limit as x approaches 0 of x^2cos(2/x)	\lim\:_{x\to\:0}(x^{2}\cos(\frac{2}{x}))
limit as x approaches-4 of \|x+4\|	\lim\:_{x\to\:-4}(\left\|x+4\right\|)
derivative of (2x)/((x+1))	derivative\:\frac{2x}{(x+1)}
integral of 9x^3e^{3x}	\int\:9x^{3}e^{3x}dx
sum from n=1 to infinity of 1/(3^n+n)	\sum\:_{n=1}^{\infty\:}\frac{1}{3^{n}+n}
tangent of f(x)=x^2+3,\at x=-1	tangent\:f(x)=x^{2}+3,\at\:x=-1
derivative of f(x)=(3x^6+2x^3)^4	derivative\:f(x)=(3x^{6}+2x^{3})^{4}
(dy)/(dx)=y(3y-6)	\frac{dy}{dx}=y(3y-6)
derivative of 1/(3x^4+1)	\frac{d}{dx}(\frac{1}{3x^{4}+1})
integral of 1/(\sqrt[3]{x)+5}	\int\:\frac{1}{\sqrt[3]{x}+5}dx
integral of sec^2(2x)-1	\int\:\sec^{2}(2x)-1dx
integral of tan^2(x)sec^{10}(x)	\int\:\tan^{2}(x)\sec^{10}(x)dx
limit as x approaches 0+of (tan(x))/x	\lim\:_{x\to\:0+}(\frac{\tan(x)}{x})
y^{''''}+50y^{''}+625y=0	y^{\prime\:\prime\:\prime\:\prime\:}+50y^{\prime\:\prime\:}+625y=0
limit as x approaches 3 of 2x^3-10x-12	\lim\:_{x\to\:3}(2x^{3}-10x-12)
limit as x approaches 2 of 4+5(-2)	\lim\:_{x\to\:2}(4+5(-2))
integral of 2sec^3(x)	\int\:2\sec^{3}(x)dx
(\partial)/(\partial x)((10x)/(36+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{10x}{36+x^{2}+y^{2}})
integral of (x^2-4x)e^{2x}	\int\:(x^{2}-4x)e^{2x}dx
sum from n=1 to infinity of (10^n)/(n^n)	\sum\:_{n=1}^{\infty\:}\frac{10^{n}}{n^{n}}
derivative of 4x^4	derivative\:4x^{4}
ye^ydx+(1+xe^y)dy=0,y(5)=0,y=y	y\cdot\:e^{y}dx+(1+x\cdot\:e^{y})dy=0,y(5)=0,y=y
derivative of f(t)=8t-9t^2	derivative\:f(t)=8t-9t^{2}
(\partial)/(\partial x)(e^{xy}+2x-5y)	\frac{\partial\:}{\partial\:x}(e^{xy}+2x-5y)
y^{''}+8y^'+7y=0,y(0)=6,y^'(0)=-1	y^{\prime\:\prime\:}+8y^{\prime\:}+7y=0,y(0)=6,y^{\prime\:}(0)=-1
(d^2)/(dx^2)(x^4-6x^3)	\frac{d^{2}}{dx^{2}}(x^{4}-6x^{3})
(\partial)/(\partial x)((7x)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{7x}{x^{2}+y^{2}})
laplacetransform sin(6(t-(5pi)/6))	laplacetransform\:\sin(6(t-\frac{5π}{6}))
inverse oflaplace 1/(s(1+s))	inverselaplace\:\frac{1}{s(1+s)}
area y=x,y= x/3 ,y=2	area\:y=x,y=\frac{x}{3},y=2
integral from 0 to 2 of x^2sqrt(1+x^3)	\int\:_{0}^{2}x^{2}\sqrt{1+x^{3}}dx
derivative of 2/(1+4x^2)	\frac{d}{dx}(\frac{2}{1+4x^{2}})
integral of (x^2)/(sqrt(36+x^2))	\int\:\frac{x^{2}}{\sqrt{36+x^{2}}}dx
derivative of x^3-5	derivative\:x^{3}-5
inverse oflaplace (3s-1)/(s^2-1)	inverselaplace\:\frac{3s-1}{s^{2}-1}
(\partial)/(\partial x)(((x+y))/(y+z))	\frac{\partial\:}{\partial\:x}(\frac{(x+y)}{y+z})
(dy)/(dx)=(yx)/(x-1)	\frac{dy}{dx}=\frac{yx}{x-1}
integral of ((cos(x)))/(sin^2(x))	\int\:\frac{(\cos(x))}{\sin^{2}(x)}dx
integral of 2sin^2(xco)s^3x	\int\:2\sin^{2}(xco)s^{3}xdx
y^'+5y=2xy^5	y^{\prime\:}+5y=2xy^{5}
(dy)/(dx)+2x^{-1}y=6x^4y^2	\frac{dy}{dx}+2x^{-1}y=6x^{4}y^{2}
(1/8)y^{''}+4y^'+20y=0	(\frac{1}{8})y^{\prime\:\prime\:}+4y^{\prime\:}+20y=0
integral of 30(x+9)(x+9)^4	\int\:30(x+9)(x+9)^{4}dx
derivative of (x^3/2-3/(x^2))	\frac{d}{dx}(\frac{x^{3}}{2}-\frac{3}{x^{2}})
y^{''}-7y^'+10y=-2cos(2t)	y^{\prime\:\prime\:}-7y^{\prime\:}+10y=-2\cos(2t)
derivative of f(x)=4x-1	derivative\:f(x)=4x-1
(dy)/(dx)=8e^{x-y}	\frac{dy}{dx}=8e^{x-y}
integral of 3v(v^2+4)^2	\int\:3v(v^{2}+4)^{2}dv
integral of x^25^x	\int\:x^{2}5^{x}dx
integral of (10)/(sqrt(x))	\int\:\frac{10}{\sqrt{x}}dx
integral from 0 to 2 of e^x	\int\:_{0}^{2}e^{x}dx
limit as x approaches 0 of 3/(x^2+x)-3/x	\lim\:_{x\to\:0}(\frac{3}{x^{2}+x}-\frac{3}{x})
integral from-1 to 1 of 2/(1+x^2)	\int\:_{-1}^{1}\frac{2}{1+x^{2}}dx
(dx)/(dt)=12-(27x)/(900-15t)	\frac{dx}{dt}=12-\frac{27x}{900-15t}

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