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Popular Calculus Problems

integral of e^{2ln(y)}*e^y	\int\:e^{2\ln(y)}\cdot\:e^{y}dy
limit as x approaches-1 of (x^2-4)/(1-x)	\lim\:_{x\to\:-1}(\frac{x^{2}-4}{1-x})
derivative of 7xe^{6x}	derivative\:7xe^{6x}
derivative of x^{1/2}	derivative\:x^{\frac{1}{2}}
derivative of 4sin(x)	derivative\:4\sin(x)
derivative of 4x+(600/x+308)	\frac{d}{dx}(4x+\frac{600}{x}+308)
y^'+1/x y= 7/(x^2)+3	y^{\prime\:}+\frac{1}{x}y=\frac{7}{x^{2}}+3
limit as x approaches 0 of 1/2+x^2	\lim\:_{x\to\:0}(\frac{1}{2}+x^{2})
(\partial)/(\partial x)((x-y)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{x-y}{x+y})
derivative of f(x)=((x^2-1))/(2x-3)	derivative\:f(x)=\frac{(x^{2}-1)}{2x-3}
derivative of (ln(x)^2)	\frac{d}{dx}((\ln(x))^{2})
integral of (6x)/(x^3-8)	\int\:\frac{6x}{x^{3}-8}dx
integral from 0 to 2 of (sqrt(4-x^2))	\int\:_{0}^{2}(\sqrt{4-x^{2}})dx
laplacetransform 10x	laplacetransform\:10x
(dy)/(dx)+2xy=2xe^{-x^2}	\frac{dy}{dx}+2xy=2xe^{-x^{2}}
integral of cos(y^2)	\int\:\cos(y^{2})dy
8y^{''}+32y^'=0,y(2)=1,y^'(-1)=1	8y^{\prime\:\prime\:}+32y^{\prime\:}=0,y(2)=1,y^{\prime\:}(-1)=1
derivative of x^3-sqrt(x)	derivative\:x^{3}-\sqrt{x}
integral of sin(4x)cos(2x)	\int\:\sin(4x)\cos(2x)dx
derivative of (9cos(x))/(1+sin(x))	derivative\:\frac{9\cos(x)}{1+\sin(x)}
limit as x approaches 6 of ln(x-6)	\lim\:_{x\to\:6}(\ln(x-6))
area 17x,x^2	area\:17x,x^{2}
derivative of f(x)= 1/(\sqrt[3]{x)}	derivative\:f(x)=\frac{1}{\sqrt[3]{x}}
sum from n=1 to infinity of (e^n)/(n^n)	\sum\:_{n=1}^{\infty\:}\frac{e^{n}}{n^{n}}
(dy)/(dx)=(x+1)^3	\frac{dy}{dx}=(x+1)^{3}
integral of (1/(cos(4x)))^2	\int\:(\frac{1}{\cos(4x)})^{2}dx
y'=0.0012y(1000-y)	y\prime\:=0.0012y(1000-y)
derivative of xe^x+x	\frac{d}{dx}(xe^{x}+x)
integral of arctan(4t)	\int\:\arctan(4t)dt
sum from n=3 to infinity of 1/(ln(n))	\sum\:_{n=3}^{\infty\:}\frac{1}{\ln(n)}
(\partial)/(\partial x)((e^x+e^y)^5)	\frac{\partial\:}{\partial\:x}((e^{x}+e^{y})^{5})
integral from 1 to 3 of (4x^3-3x^2)	\int\:_{1}^{3}(4x^{3}-3x^{2})dx
inverse oflaplace 1/(s^2+s)	inverselaplace\:\frac{1}{s^{2}+s}
sum from n=1 to infinity of-1/(n^2)	\sum\:_{n=1}^{\infty\:}-\frac{1}{n^{2}}
derivative of x^{10x}	derivative\:x^{10x}
derivative of 3x+10	derivative\:3x+10
integral of (-1/5 sec(1-5x))	\int\:(-\frac{1}{5}\sec(1-5x))dx
limit as x approaches 1 of (ln(x))^{1-x}	\lim\:_{x\to\:1}((\ln(x))^{1-x})
integral of e^{14x}	\int\:e^{14x}dx
derivative of (x^2+3(x^2-4x))	\frac{d}{dx}((x^{2}+3)(x^{2}-4x))
limit as x approaches-3+of 1/(6+2x)	\lim\:_{x\to\:-3+}(\frac{1}{6+2x})
taylor 3sin(-x)	taylor\:3\sin(-x)
tangent of f(x)=3x^2,\at x=10	tangent\:f(x)=3x^{2},\at\:x=10
integral from 1 to 10 of (37)/(x^3)	\int\:_{1}^{10}\frac{37}{x^{3}}dx
derivative of ln((2x+1/(2x-1)))	\frac{d}{dx}(\ln(\frac{2x+1}{2x-1}))
limit as x approaches a of 1-sqrt(1-x^2)	\lim\:_{x\to\:a}(1-\sqrt{1-x^{2}})
xydx+(x+1)dy=0	xydx+(x+1)dy=0
derivative of (e^x/(x-1))	\frac{d}{dx}(\frac{e^{x}}{x-1})
derivative of cos^5(3x)	\frac{d}{dx}(\cos^{5}(3x))
(\partial)/(\partial x)(9)	\frac{\partial\:}{\partial\:x}(9)
y^'=a^{x+y}	y^{\prime\:}=a^{x+y}
integral of x/(sqrt(x-x^2))	\int\:\frac{x}{\sqrt{x-x^{2}}}dx
derivative of 6ln(4x)	\frac{d}{dx}(6\ln(4x))
(dy)/(dx)=85yx^{16}	\frac{dy}{dx}=85yx^{16}
(dy)/(dt)=-5y	\frac{dy}{dt}=-5y
sum from n=0 to infinity of 2*(2/5)^n	\sum\:_{n=0}^{\infty\:}2\cdot\:(\frac{2}{5})^{n}
derivative of tan(x^5)	derivative\:\tan(x^{5})
integral of (5/(t^2)-8t^6)	\int\:(\frac{5}{t^{2}}-8t^{6})dt
limit as x approaches 0 of (x_{-1})/x	\lim\:_{x\to\:0}(\frac{x_{-1}}{x})
derivative of 6sin^2(t)	derivative\:6\sin^{2}(t)
integral of (3x+15)sqrt(x^2+10x+4)	\int\:(3x+15)\sqrt{x^{2}+10x+4}dx
integral of (e^{2t})	\int\:(e^{2t})dt
derivative of (sin(3x))/(tan(4x))	derivative\:\frac{\sin(3x)}{\tan(4x)}
taylor 1/(x-1),21	taylor\:\frac{1}{x-1},21
integral from 0 to 1/6 of 3/(sqrt(1-9x^2))	\int\:_{0}^{\frac{1}{6}}\frac{3}{\sqrt{1-9x^{2}}}dx
(dx)/(dt)=xt	\frac{dx}{dt}=xt
y^{''}-2y^'+1y=0,y(0)=8,y^'(0)=2	y^{\prime\:\prime\:}-2y^{\prime\:}+1y=0,y(0)=8,y^{\prime\:}(0)=2
integral of-8x^2	\int\:-8x^{2}dx
inverse oflaplace (e^{-pi(s)})/(s^3+s)	inverselaplace\:\frac{e^{-π(s)}}{s^{3}+s}
derivative of (x+1/x ^5)	\frac{d}{dx}((x+\frac{1}{x})^{5})
integral from 0 to infinity of ue^{-u^2}	\int\:_{0}^{\infty\:}ue^{-u^{2}}du
inverse oflaplace s/(s^2+10s+9.8)	inverselaplace\:\frac{s}{s^{2}+10s+9.8}
(dy)/(dx)=2*y/x+(y/x)^2	\frac{dy}{dx}=2\cdot\:\frac{y}{x}+(\frac{y}{x})^{2}
limit as x approaches 1+of (ln(x))/(x-1)	\lim\:_{x\to\:1+}(\frac{\ln(x)}{x-1})
limit as x approaches 0 of 6/(x^2+x)-6/x	\lim\:_{x\to\:0}(\frac{6}{x^{2}+x}-\frac{6}{x})
integral from-1 to 3 of x(x-1)(x+2)	\int\:_{-1}^{3}x(x-1)(x+2)dx
integral of x^3sqrt(x^2+19)	\int\:x^{3}\sqrt{x^{2}+19}dx
tangent of y= 4/(5x+1),(-1,-1)	tangent\:y=\frac{4}{5x+1},(-1,-1)
derivative of 9/(x^2)-3/x	derivative\:\frac{9}{x^{2}}-\frac{3}{x}
derivative of 2e^{-x^3}	\frac{d}{dx}(2e^{-x^{3}})
integral of-1/(v^2)	\int\:-\frac{1}{v^{2}}dv
integral from 1/2 to 1 of (x^{-3}-8)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-8)dx
(\partial)/(\partial x)(x^{-7}y^2+xy^2+2xy)	\frac{\partial\:}{\partial\:x}(x^{-7}y^{2}+xy^{2}+2xy)
limit as x approaches-3 of (x^2)/(9-x^2)	\lim\:_{x\to\:-3}(\frac{x^{2}}{9-x^{2}})
(\partial)/(\partial y)(e^{7yz})	\frac{\partial\:}{\partial\:y}(e^{7yz})
limit as x approaches 4+of (7x-1)/(x-4)	\lim\:_{x\to\:4+}(\frac{7x-1}{x-4})
derivative of sqrt(3+\sqrt{7x)}	\frac{d}{dx}(\sqrt{3+\sqrt{7x}})
integral from 0 to 0 of x^2	\int\:_{0}^{0}x^{2}dx
(\partial)/(\partial x)(ln(x/(20)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{20}))
limit as x approaches 0 of x*1/x	\lim\:_{x\to\:0}(x\cdot\:\frac{1}{x})
integral of x/((1+x)^4)	\int\:\frac{x}{(1+x)^{4}}dx
integral of sqrt(x)(x^4+1/(x^2))	\int\:\sqrt{x}(x^{4}+\frac{1}{x^{2}})dx
integral from 1 to 2 of (2/(x^3))	\int\:_{1}^{2}(\frac{2}{x^{3}})dx
derivative of f(x)=ln(x^3-1)	derivative\:f(x)=\ln(x^{3}-1)
derivative of sqrt(x)+7/(sqrt(x))	\frac{d}{dx}(\sqrt{x}+\frac{7}{\sqrt{x}})
derivative of (x-2pi^2)	\frac{d}{dx}((x-2π)^{2})
limit as x approaches 5 of (3+1/x)^3	\lim\:_{x\to\:5}((3+\frac{1}{x})^{3})
y^'=(4x)/(e^x)	y^{\prime\:}=\frac{4x}{e^{x}}
derivative of x^2(1-9x)	derivative\:x^{2}(1-9x)
derivative of f(x)=x^4-20x^2+64	derivative\:f(x)=x^{4}-20x^{2}+64

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