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Popular Calculus Problems

integral of (\sqrt[4]{x^3}+(10)/(x^2))	\int\:(\sqrt[4]{x^{3}}+\frac{10}{x^{2}})dx
integral of 15sec^5(x)	\int\:15\sec^{5}(x)dx
derivative of cos(x(sin(x)))	\frac{d}{dx}(\cos(x)(\sin(x)))
integral from 0 to pi/(12) of cos(6x)	\int\:_{0}^{\frac{π}{12}}\cos(6x)dx
integral from 0 to 2 of x3^x	\int\:_{0}^{2}x3^{x}dx
integral of ((x^2+2))/(x+2)	\int\:\frac{(x^{2}+2)}{x+2}dx
(\partial)/(\partial x)(((x-y))/(ln(x/y)))	\frac{\partial\:}{\partial\:x}(\frac{(x-y)}{\ln(\frac{x}{y})})
2(d^2y)/(dx^2)-20(dy)/(dx)+48y=3sin(5x)	2\frac{d^{2}y}{dx^{2}}-20\frac{dy}{dx}+48y=3\sin(5x)
inverse oflaplace s/(s^2+2s+2)	inverselaplace\:\frac{s}{s^{2}+2s+2}
integral of (y/2-tan(x))y	\int\:(\frac{y}{2}-\tan(x))ydx
y^{''}-7y+10y=0	y^{\prime\:\prime\:}-7y+10y=0
integral of 5/(1+5x)	\int\:\frac{5}{1+5x}dx
derivative of f(x)=x^7-1/(x^7)	derivative\:f(x)=x^{7}-\frac{1}{x^{7}}
derivative of 3/x-2	\frac{d}{dx}(\frac{3}{x}-2)
(dy)/(dx)=e^{2x}	\frac{dy}{dx}=e^{2x}
simplify x/(sqrt(7-3x))	simplify\:\frac{x}{\sqrt{7-3x}}
integral of (2y)/((x^2+y^2)^2)	\int\:\frac{2y}{(x^{2}+y^{2})^{2}}dy
derivative of (sqrt(x)/(7+x))	\frac{d}{dx}(\frac{\sqrt{x}}{7+x})
derivative of 8/(x^9)	\frac{d}{dx}(\frac{8}{x^{9}})
(\partial)/(\partial x)((e^x+e^y)^4)	\frac{\partial\:}{\partial\:x}((e^{x}+e^{y})^{4})
derivative of sqrt(7x+9)	\frac{d}{dx}(\sqrt{7x+9})
derivative of f(t)=(1+sqrt(t))(2t^2-7)	derivative\:f(t)=(1+\sqrt{t})(2t^{2}-7)
integral of x^1((5x^2+2/3)^4)/1	\int\:x^{1}\frac{(5x^{2}+\frac{2}{3})^{4}}{1}dx
d/(dt)((d/(dt)(e^tcos(t)))^2)	\frac{d}{dt}((\frac{d}{dt}(e^{t}\cos(t)))^{2})
derivative of f(x)=(e^{x^2})/(x^3)	derivative\:f(x)=\frac{e^{x^{2}}}{x^{3}}
limit as x approaches 0 of xln(1-2/(3w(x)))	\lim\:_{x\to\:0}(x\ln(1-\frac{2}{3w(x)}))
limit as x approaches-3 of 2x^2-3x+4	\lim\:_{x\to\:-3}(2x^{2}-3x+4)
derivative of x^3-9x^2+24x-15	\frac{d}{dx}(x^{3}-9x^{2}+24x-15)
y^{''}+2y^'+2y=sin(x),y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(x),y(0)=0,y^{\prime\:}(0)=0
integral of u/(sqrt(1+u^2))	\int\:\frac{u}{\sqrt{1+u^{2}}}du
derivative of f(x)=x^3-12x	derivative\:f(x)=x^{3}-12x
derivative of 2sqrt(cos(2x))	\frac{d}{dx}(2\sqrt{\cos(2x)})
derivative of 4/x+5/(x^2)	\frac{d}{dx}(\frac{4}{x}+\frac{5}{x^{2}})
(\partial)/(\partial x)(1+xln(xy-7))	\frac{\partial\:}{\partial\:x}(1+x\ln(xy-7))
(dx)/(dt)=30-(3x)/(100)	\frac{dx}{dt}=30-\frac{3x}{100}
limit as x approaches 2 of 3*6+6.6	\lim\:_{x\to\:2}(3\cdot\:6+6.6)
derivative of e^{\sqrt[3]{5x}}	\frac{d}{dx}(e^{\sqrt[3]{5x}})
derivative of f(x)=168(2x+5)^5	derivative\:f(x)=168(2x+5)^{5}
3y^{''}+y^'=0	3y^{\prime\:\prime\:}+y^{\prime\:}=0
derivative of 3x^2-2x+1	\frac{d}{dx}(3x^{2}-2x+1)
y^'cot(x)+y=2	y^{\prime\:}\cot(x)+y=2
derivative of (sin(2x)/(5x^2))	\frac{d}{dx}(\frac{\sin(2x)}{5x^{2}})
integral of 6x^3e^{-x^2}	\int\:6x^{3}e^{-x^{2}}dx
d/(dz)(cos(z))	\frac{d}{dz}(\cos(z))
limit as x approaches 0 of pi	\lim\:_{x\to\:0}(π)
derivative of y=ln((7+e^x)/(7-e^x))	derivative\:y=\ln(\frac{7+e^{x}}{7-e^{x}})
integral of cos^2(x	\int\:\cos^{2}(d)xdx
y^'+0.121y=-3	y^{\prime\:}+0.121y=-3
y^'=((3x^7e^{y/x}+x^5y^2))/(x^6y)	y^{\prime\:}=\frac{(3x^{7}e^{\frac{y}{x}}+x^{5}y^{2})}{x^{6}y}
(\partial)/(\partial x)(1/(x+ct))	\frac{\partial\:}{\partial\:x}(\frac{1}{x+ct})
integral from ln(2) to 3 of (5e^x)	\int\:_{\ln(2)}^{3}(5e^{x})dx
limit as x approaches 2 of x-3	\lim\:_{x\to\:2}(x-3)
integral from 0 to 1 of (x^2-x^3)	\int\:_{0}^{1}(x^{2}-x^{3})dx
limit as x approaches 0 of (1-cos(7x))/(4x^2)	\lim\:_{x\to\:0}(\frac{1-\cos(7x)}{4x^{2}})
derivative of A(2xe^x+e^xx^2)	\frac{d}{dx}(A(2xe^{x}+e^{x}x^{2}))
limit as x approaches 2 of 1/2	\lim\:_{x\to\:2}(\frac{1}{2})
derivative of-x^{2/3}(x-4)	\frac{d}{dx}(-x^{\frac{2}{3}}(x-4))
integral of 3/2 sqrt(x)	\int\:\frac{3}{2}\sqrt{x}dx
integral of (2x-x^2)^2	\int\:(2x-x^{2})^{2}dx
derivative of sqrt(2ax-x^2)	\frac{d}{dx}(\sqrt{2ax-x^{2}})
area x=((y-3)^2)/5 ,x=13-y	area\:x=\frac{(y-3)^{2}}{5},x=13-y
derivative of 3/4 x^{1/2}	\frac{d}{dx}(\frac{3}{4}x^{\frac{1}{2}})
integral from 0 to 8 of 9/(10x^2+11x+1)	\int\:_{0}^{8}\frac{9}{10x^{2}+11x+1}dx
(dy)/(dx)=(x^2)/(6e^y)	\frac{dy}{dx}=\frac{x^{2}}{6e^{y}}
derivative of f(x)=4x^2-7x	derivative\:f(x)=4x^{2}-7x
laplacetransform 3tsin(t)	laplacetransform\:3t\sin(t)
(\partial)/(\partial x)((5y)/(x^5))	\frac{\partial\:}{\partial\:x}(\frac{5y}{x^{5}})
xy^'-3y^2=0	xy^{\prime\:}-3y^{2}=0
laplacetransform 3e^{-7t}cos(t/3+pi/3)	laplacetransform\:3e^{-7t}\cos(\frac{t}{3}+\frac{π}{3})
(dy)/(dx-y^2)=36	\frac{dy}{dx-y^{2}}=36
limit as x approaches 0 of (cos(4x)-1)/x	\lim\:_{x\to\:0}(\frac{\cos(4x)-1}{x})
(\partial)/(\partial y)(2xsin(y))	\frac{\partial\:}{\partial\:y}(2x\sin(y))
limit as v approaches 4+of (4-v)/(\|4-v\|)	\lim\:_{v\to\:4+}(\frac{4-v}{\left\|4-v\right\|})
(\partial)/(\partial x)(x^2+5)	\frac{\partial\:}{\partial\:x}(x^{2}+5)
inverse oflaplace cos^2(8t)	inverselaplace\:\cos^{2}(8t)
integral from-1 to 1 of (x^2)	\int\:_{-1}^{1}(x^{2})dx
derivative of (e^{3x}/(x^{12)})	\frac{d}{dx}(\frac{e^{3x}}{x^{12}})
derivative of 2/((3x^2))	\frac{d}{dx}(\frac{2}{(3x)^{2}})
limit as x approaches 0.1 of (5sin(x))/x	\lim\:_{x\to\:0.1}(\frac{5\sin(x)}{x})
limit as x approaches 6 of (x^2-3x-18)/(x-6)	\lim\:_{x\to\:6}(\frac{x^{2}-3x-18}{x-6})
slope of (-3.2)(6.3)	slope\:(-3.2)(6.3)
integral from pi/4 to pi of sin(2x)	\int\:_{\frac{π}{4}}^{π}\sin(2x)dx
derivative of e^{7/x}	derivative\:e^{\frac{7}{x}}
sum from n=0 to infinity of ln(1/(n+1))	\sum\:_{n=0}^{\infty\:}\ln(\frac{1}{n+1})
(dy)/(dx)=(2xy-y^2)/(2xy-x^2)	\frac{dy}{dx}=\frac{2xy-y^{2}}{2xy-x^{2}}
derivative of y=8xsin(x)	derivative\:y=8x\sin(x)
limit as x approaches 0 of (sin(3)(x))/x	\lim\:_{x\to\:0}(\frac{\sin(3)(x)}{x})
integral of xsqrt(x^4-9)	\int\:x\sqrt{x^{4}-9}dx
integral from 0 to 3 of (x^2-2x)	\int\:_{0}^{3}(x^{2}-2x)dx
y^{''}+11y^'-28y=0	y^{\prime\:\prime\:}+11y^{\prime\:}-28y=0
integral of 8/(x^5)	\int\:\frac{8}{x^{5}}dx
limit as x approaches 3 of (x^2-9)/(x^2-10x+21)	\lim\:_{x\to\:3}(\frac{x^{2}-9}{x^{2}-10x+21})
integral of 1/()	\int\:\frac{1}{dx}dt
derivative of y=e^{-x}sin(x)	derivative\:y=e^{-x}\sin(x)
integral of-1/(1+y^2)	\int\:-\frac{1}{1+y^{2}}dy
integral of x^{10/3}	\int\:x^{\frac{10}{3}}dx
integral of (12+10x-2x^2)/(x^3-4x)	\int\:\frac{12+10x-2x^{2}}{x^{3}-4x}dx
laplacetransform xe^{3x+4}-x^2	laplacetransform\:xe^{3x+4}-x^{2}
derivative of e^{x^4+5x}	\frac{d}{dx}(e^{x^{4}+5x})
y^{''}+12y^'+100y=0	y^{\prime\:\prime\:}+12y^{\prime\:}+100y=0

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