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Popular Calculus Problems

integral of cos(x)(9+5sin^2(x))	\int\:\cos(x)(9+5\sin^{2}(x))dx
integral of sin(xy)+xycos(xy)	\int\:\sin(xy)+xy\cos(xy)dx
integral from 3 to 7 of ((2x-3))/6	\int\:_{3}^{7}\frac{(2x-3)}{6}dx
integral of (x+6)/(sqrt(5-4x-x^2))	\int\:\frac{x+6}{\sqrt{5-4x-x^{2}}}dx
d/(dt)(ln(cos(pi/2-t/2)))	\frac{d}{dt}(\ln(\cos(\frac{π}{2}-\frac{t}{2})))
integral of (x+2)e^{4-3x}	\int\:(x+2)e^{4-3x}dx
sum from n=1 to infinity of (3^n)/n	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{n}
laplacetransform (t-1)cos(4(t-1))	laplacetransform\:(t-1)\cos(4(t-1))
(x-1)y^'+xy=6e^x	(x-1)y^{\prime\:}+xy=6e^{x}
sum from n=1 to infinity of (n!)/(n^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{n^{n}}
integral of tan^3(x)(sec(x))^{-1/2}	\int\:\tan^{3}(x)(\sec(x))^{-\frac{1}{2}}dx
integral from 0 to 2 of (2+x)	\int\:_{0}^{2}(2+x)dx
derivative of 5e^x+x	derivative\:5e^{x}+x
integral of k*x	\int\:k\cdot\:xdx
limit as (x,y) approaches (0,4) of x^3y	\lim\:_{(x,y)\to\:(0,4)}(x^{3}y)
area f(x)=ln(2),y=0,y=2	area\:f(x)=\ln(2),y=0,y=2
integral from 0 to 1 of (x^2+6)e^{-x}	\int\:_{0}^{1}(x^{2}+6)e^{-x}dx
slope of y= 1/(x-5)	slope\:y=\frac{1}{x-5}
integral from 0 to ln(4) of e^{-2x}	\int\:_{0}^{\ln(4)}e^{-2x}dx
derivative of e^{tan(x})	\frac{d}{dx}(e^{\tan(x)})
derivative of xsqrt(400-x^2)	\frac{d}{dx}(x\sqrt{400-x^{2}})
5y^'+15y=375,y(0)=0	5y^{\prime\:}+15y=375,y(0)=0
taylor e^x,1	taylor\:e^{x},1
sum from n=0 to infinity of-n/(2^n)	\sum\:_{n=0}^{\infty\:}-\frac{n}{2^{n}}
area x^4-2x^2,2x^2	area\:x^{4}-2x^{2},2x^{2}
limit as x approaches infinity of x^n	\lim\:_{x\to\:\infty\:}(x^{n})
integral of cos^5(θ)sin(2θ)	\int\:\cos^{5}(θ)\sin(2θ)dθ
integral of (x^2)/(1-x^2)	\int\:\frac{x^{2}}{1-x^{2}}dx
integral of 5tan^3(x)	\int\:5\tan^{3}(x)dx
limit as x approaches 0 of 2/((x-5)^6)	\lim\:_{x\to\:0}(\frac{2}{(x-5)^{6}})
-3y^'+(2y)/x =(y^4)/(x^4)	-3y^{\prime\:}+\frac{2y}{x}=\frac{y^{4}}{x^{4}}
y^{''}-3y^'-4y=12	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=12
(\partial)/(\partial y)(5x^2+y^2)	\frac{\partial\:}{\partial\:y}(5x^{2}+y^{2})
area y=0,y=9-x^2	area\:y=0,y=9-x^{2}
integral of cos^2(x)+1	\int\:\cos^{2}(x)+1dx
derivative of y=-4log_{5}(x)	derivative\:y=-4\log_{5}(x)
derivative of e^{3x}+e^{x+e^{-2x}}	\frac{d}{dx}(e^{3x}+e^{x+e^{-2x}})
integral from 1 to e of t^2ln(t)	\int\:_{1}^{e}t^{2}\ln(t)dt
derivative of (x-3)/x	derivative\:\frac{x-3}{x}
integral of 1/(x^2+4x+2)	\int\:\frac{1}{x^{2}+4x+2}dx
x^3y^'+2x^2y=4cos(4x)y^{-1/2}	x^{3}y^{\prime\:}+2x^{2}y=4\cos(4x)y^{-\frac{1}{2}}
derivative of f(x)=sqrt(log_{a)(x)}	derivative\:f(x)=\sqrt{\log_{a}(x)}
(\partial)/(\partial x)(x^{1/2}+y)	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}+y)
tangent of y=4e^x	tangent\:y=4e^{x}
(\partial)/(\partial t)(t^2)	\frac{\partial\:}{\partial\:t}(t^{2})
limit as x approaches 0 of arctan(6x)	\lim\:_{x\to\:0}(\arctan(6x))
limit as x approaches-3 of 5-x	\lim\:_{x\to\:-3}(5-x)
d/(dy)(1/(x+y))	\frac{d}{dy}(\frac{1}{x+y})
derivative of (-2+x^2^{-1})	\frac{d}{dx}((-2+x^{2})^{-1})
25y^{''}+80y^'+64y=0	25y^{\prime\:\prime\:}+80y^{\prime\:}+64y=0
integral of x^3sqrt(169-x^2)	\int\:x^{3}\sqrt{169-x^{2}}dx
derivative of 2/(2x)	\frac{d}{dx}(\frac{2}{2x})
derivative of 2sin(x-sqrt(3))	\frac{d}{dx}(2\sin(x)-\sqrt{3})
slope of y= 6/((x-1)^2),\at	slope\:y=\frac{6}{(x-1)^{2}},\at\:
derivative of (sec(4x+tan(2x))^5)	\frac{d}{dx}((\sec(4x)+\tan(2x))^{5})
derivative of (x^2+3x(x-2)(x^2+1))	\frac{d}{dx}((x^{2}+3x)(x-2)(x^{2}+1))
area y=2x-x^2,(0,2)	area\:y=2x-x^{2},(0,2)
derivative of 9sin(3x)	derivative\:9\sin(3x)
integral from 0 to 1 of-x+2	\int\:_{0}^{1}-x+2dx
f(x)=log_{3}(4x^2+2x)	f(x)=\log_{3}(4x^{2}+2x)
inverse oflaplace (-40x-80)/(x^2+3x+1)	inverselaplace\:\frac{-40x-80}{x^{2}+3x+1}
(1/4)y^{''}+y^'+y=x^2-2x	(\frac{1}{4})y^{\prime\:\prime\:}+y^{\prime\:}+y=x^{2}-2x
(dx)/(sqrt(1-x^2))=(dy)/(sqrt(1-y^2))	\frac{dx}{\sqrt{1-x^{2}}}=\frac{dy}{\sqrt{1-y^{2}}}
integral of (7x)/((x^2+7)^2)	\int\:\frac{7x}{(x^{2}+7)^{2}}dx
integral of (x^3+5)^2	\int\:(x^{3}+5)^{2}dx
derivative of (x+4)^6(x-3)^3	derivative\:(x+4)^{6}(x-3)^{3}
derivative of cos(tan^3(x))	derivative\:\cos(\tan^{3}(x))
laplacetransform 10e^{-t/2}	laplacetransform\:10e^{-\frac{t}{2}}
integral of cos(x)5x)	\int\:\cos(x)d(5x)dx
inverse oflaplace {s/(s^2+2s-3)}	inverselaplace\:\left\{\frac{s}{s^{2}+2s-3}\right\}
integral of ln(s)ecxtan(x)	\int\:\ln(s)ecx\tan(x)dx
tangent of 10x^3-30x+120	tangent\:10x^{3}-30x+120
derivative of 2x^2y^2	\frac{d}{dx}(2x^{2}y^{2})
derivative of sqrt(z+3)(1/(z^2))	derivative\:\sqrt{z+3}(\frac{1}{z^{2}})
(dy)/(dx)+ytan(x)=2xcos(x)	\frac{dy}{dx}+y\tan(x)=2x\cos(x)
(\partial)/(\partial z)(xy+yz+xz)	\frac{\partial\:}{\partial\:z}(xy+yz+xz)
integral of 1/3 x^3	\int\:\frac{1}{3}x^{3}dx
integral from 0 to 1 of 6/(sqrt(1-x^2))	\int\:_{0}^{1}\frac{6}{\sqrt{1-x^{2}}}dx
(\partial)/(\partial x)(arcsin(x/l))	\frac{\partial\:}{\partial\:x}(\arcsin(\frac{x}{l}))
derivative of 3/(5x^{2/5})	\frac{d}{dx}(\frac{3}{5x^{\frac{2}{5}}})
integral of (2x^4)/(\sqrt[3]{x^2)}	\int\:\frac{2x^{4}}{\sqrt[3]{x^{2}}}dx
integral of ((e^x)/2+xsqrt(x))	\int\:(\frac{e^{x}}{2}+x\sqrt{x})dx
y^'=(4x^7e^{y/x}+x^5y^2)/(x^6y)	y^{\prime\:}=\frac{4x^{7}e^{\frac{y}{x}}+x^{5}y^{2}}{x^{6}y}
derivative of (sin(x)/(ln(x)))	\frac{d}{dx}(\frac{\sin(x)}{\ln(x)})
derivative of arctan(2x^2-4)	\frac{d}{dx}(\arctan(2x^{2}-4))
y^{''}-8y^'+16=0	y^{\prime\:\prime\:}-8y^{\prime\:}+16=0
limit as x approaches pi of (pi-x)cot(x)	\lim\:_{x\to\:π}((π-x)\cot(x))
laplacetransform (e^{-1})(sin(2t))	laplacetransform\:(e^{-1})(\sin(2t))
derivative of e^{8x}cos(11x)	derivative\:e^{8x}\cos(11x)
integral of X^{-1}	\int\:X^{-1}dX
roots 3xy	roots\:3xy
integral of 1/(1+sqrt(x+1))	\int\:\frac{1}{1+\sqrt{x+1}}dx
derivative of ln(x^2y^2)	\frac{d}{dx}(\ln(x^{2}y^{2}))
derivative of \sqrt[3]{x^2}+2sqrt(x^5)	\frac{d}{dx}(\sqrt[3]{x^{2}}+2\sqrt{x^{5}})
limit as x approaches infinity of (3x^2+10x-7)/(2x^2-5x)	\lim\:_{x\to\:\infty\:}(\frac{3x^{2}+10x-7}{2x^{2}-5x})
y^{''}-6y^'+25y=-45cos(2t)+30sin(2t)	y^{\prime\:\prime\:}-6y^{\prime\:}+25y=-45\cos(2t)+30\sin(2t)
derivative of ln(coth(x))	\frac{d}{dx}(\ln(\coth(x)))
integral of (cos(5x))/(e^{sin(5x))}	\int\:\frac{\cos(5x)}{e^{\sin(5x)}}dx
(dy)/(dx)=9x+y	\frac{dy}{dx}=9x+y
limit as x approaches 0 of (x-1)^2	\lim\:_{x\to\:0}((x-1)^{2})

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