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Popular Calculus Problems

integral of k/(x^6)	\int\:\frac{k}{x^{6}}dx
derivative of 1/3 (x^2+2^{3/2})	\frac{d}{dx}(\frac{1}{3}(x^{2}+2)^{\frac{3}{2}})
integral of-(4000x)/((1+x^2))	\int\:-\frac{4000x}{(1+x^{2})}dx
integral of 3/(2+x)	\int\:\frac{3}{2+x}dx
(dy)/(dx)+10tan(10x)y=5cos(10x)	\frac{dy}{dx}+10\tan(10x)y=5\cos(10x)
y^'=y^2sin(t)	y^{\prime\:}=y^{2}\sin(t)
limit as x approaches 0 of xcsc(4x)	\lim\:_{x\to\:0}(x\csc(4x))
laplacetransform 11	laplacetransform\:11
derivative of (2x/(sqrt(4x-1)))	\frac{d}{dx}(\frac{2x}{\sqrt{4x-1}})
derivative of y,(9xe^{-1/(y^3)}-20x^3)	derivative\:y,(9xe^{-\frac{1}{y^{3}}}-20x^{3})
derivative of (3-2x^5)	\frac{d}{dx}((3-2x)^{5})
(dy)/(dx)= y/((x+y))	\frac{dy}{dx}=\frac{y}{(x+y)}
integral of (sec(x)tan(x))/(sec(x)+100)	\int\:\frac{\sec(x)\tan(x)}{\sec(x)+100}dx
integral of arcsin(5x)	\int\:\arcsin(5x)dx
integral of (ln(x^{10}))/x	\int\:\frac{\ln(x^{10})}{x}dx
inverse oflaplace (2s-6)/(s^2-9)	inverselaplace\:\frac{2s-6}{s^{2}-9}
limit as x approaches 0 of ((sin(8x)))/(3x)	\lim\:_{x\to\:0}(\frac{(\sin(8x))}{3x})
derivative of cos(3x+3)	\frac{d}{dx}(\cos(3x+3))
limit as x approaches-2+of (2x+1)/(2+x)	\lim\:_{x\to\:-2+}(\frac{2x+1}{2+x})
derivative of cos(x^2)*2x	derivative\:\cos(x^{2})\cdot\:2x
laplacetransform 16	laplacetransform\:16
derivative of e^{tan(x^3})	\frac{d}{dx}(e^{\tan(x^{3})})
integral of (2e^{2x})/(e^{2x)+10e^x+24}	\int\:\frac{2e^{2x}}{e^{2x}+10e^{x}+24}dx
derivative of-5/(x^2)	derivative\:-\frac{5}{x^{2}}
integral of 3cos((pit)/2)	\int\:3\cos(\frac{πt}{2})dt
integral of 4sin(x)cos(x)	\int\:4\sin(x)\cos(x)dx
limit as x approaches 0 of ((sin^3(2x)))/((sin^3(3x)))	\lim\:_{x\to\:0}(\frac{(\sin^{3}(2x))}{(\sin^{3}(3x))})
integral of sin(x)(x)	\int\:\sin(x)(x)dx
integral of ((x-2))/((x-1))	\int\:\frac{(x-2)}{(x-1)}dx
integral of 22e^x	\int\:22e^{x}dx
integral of (e^{x^2}-1)/x	\int\:\frac{e^{x^{2}}-1}{x}dx
derivative of a(2e^{-x}x-e^{-x}x^2)	\frac{d}{dx}(a(2e^{-x}x-e^{-x}x^{2}))
limit as x approaches 1 of sqrt(9x-5)	\lim\:_{x\to\:1}(\sqrt{9x-5})
derivative of x^3+x^2-6x	\frac{d}{dx}(x^{3}+x^{2}-6x)
derivative of h(x)=2x(6x-18)^6	derivative\:h(x)=2x(6x-18)^{6}
integral of (7-4x^3+6x^6)/(x^6)	\int\:\frac{7-4x^{3}+6x^{6}}{x^{6}}dx
3y^{''}-8y^'-3y=0,y(0)=-9,y^'(0)=8	3y^{\prime\:\prime\:}-8y^{\prime\:}-3y=0,y(0)=-9,y^{\prime\:}(0)=8
integral from 1 to 3 of ((3x^2-7)/(x^3))	\int\:_{1}^{3}(\frac{3x^{2}-7}{x^{3}})dx
integral of t^3(7+t^4)^3	\int\:t^{3}(7+t^{4})^{3}dt
limit as x approaches 1 of (x)^{1/(x-1)}	\lim\:_{x\to\:1}((x)^{\frac{1}{x-1}})
integral from 0 to 4 of 3x	\int\:_{0}^{4}3xdx
integral of x^2sqrt(36-x^2)	\int\:x^{2}\sqrt{36-x^{2}}dx
sum from n=2 to infinity of n^2	\sum\:_{n=2}^{\infty\:}n^{2}
derivative of sqrt(ax^2+\|x\|^3)	\frac{d}{dx}(\sqrt{ax^{2}+\left\|x\right\|^{3}})
(\partial)/(\partial z)(xcos(y/z))	\frac{\partial\:}{\partial\:z}(x\cos(\frac{y}{z}))
derivative of c_{1}e^{-4x}+c_{2}xe^{-4x}	\frac{d}{dx}(c_{1}e^{-4x}+c_{2}xe^{-4x})
(\partial)/(\partial y)(x^4+y^4)	\frac{\partial\:}{\partial\:y}(x^{4}+y^{4})
integral of 1/3 sin(x)	\int\:\frac{1}{3}\sin(x)dx
integral of 21tan^3(θ)	\int\:21\tan^{3}(θ)dθ
y^'-4/x y=4x^5	y^{\prime\:}-\frac{4}{x}y=4x^{5}
derivative of x/(csch(x))	\frac{d}{dx}(\frac{x}{\csch(x)})
integral of 30x*(x+1)^4	\int\:30x\cdot\:(x+1)^{4}dx
derivative of (2x/((1+x^2)^2))	\frac{d}{dx}(\frac{2x}{(1+x^{2})^{2}})
integral of (x^4)/(x^4-16)	\int\:\frac{x^{4}}{x^{4}-16}dx
y^{''}+9y=2cos(3x)+3sin(3x)	y^{\prime\:\prime\:}+9y=2\cos(3x)+3\sin(3x)
tangent of f(x)=4sin(x),\at x= pi/2	tangent\:f(x)=4\sin(x),\at\:x=\frac{π}{2}
yy^'=y^2+1	yy^{\prime\:}=y^{2}+1
derivative of f(x)=csc^3(5x^2+1)	derivative\:f(x)=\csc^{3}(5x^{2}+1)
integral of cot^4(1/2)t	\int\:\cot^{4}(\frac{1}{2})tdt
integral of (x^2-9)/(x+3)	\int\:\frac{x^{2}-9}{x+3}dx
integral of (5x+1)/(x^2-6x+13)	\int\:\frac{5x+1}{x^{2}-6x+13}dx
integral of (3e^x)/(e^{2x)+8e^x+16}	\int\:\frac{3e^{x}}{e^{2x}+8e^{x}+16}dx
integral of 4x-x^2	\int\:4x-x^{2}dx
sum from n=0 to infinity of ne^n	\sum\:_{n=0}^{\infty\:}ne^{n}
integral of x+10	\int\:x+10dx
integral from 0 to 4 of (4x-x^2)	\int\:_{0}^{4}(4x-x^{2})dx
(\partial)/(\partial x)((x^2)/(y^3))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{y^{3}})
area x^2-1, 1/2 x^2	area\:x^{2}-1,\frac{1}{2}x^{2}
integral of (sin(2x))/(2+2sin^2(x))	\int\:\frac{\sin(2x)}{2+2\sin^{2}(x)}dx
y^{''}+49y=-49sec^2(7x)	y^{\prime\:\prime\:}+49y=-49\sec^{2}(7x)
(9x^2+y-1)-(4y-x)y^'=0	(9x^{2}+y-1)-(4y-x)y^{\prime\:}=0
taylor ln(1/(1-x))	taylor\:\ln(\frac{1}{1-x})
integral of 1/(x^2)+4/(xsqrt(x))+2	\int\:\frac{1}{x^{2}}+\frac{4}{x\sqrt{x}}+2dx
integral of xe^y	\int\:xe^{y}dy
d/(dt)(ae^t)	\frac{d}{dt}(ae^{t})
(\partial)/(\partial x)(xe^{-x-y}sin(y))	\frac{\partial\:}{\partial\:x}(xe^{-x-y}\sin(y))
4x^2ydx+xydy=0	4x^{2}ydx+xydy=0
integral from 0 to 5 of te^{-t}	\int\:_{0}^{5}te^{-t}dt
derivative of ({f}(x)^4)	\frac{d}{dx}(({f}(x))^{4})
f(x)=sin(6x)	f(x)=\sin(6x)
integral of 1/(sec^2(x))	\int\:\frac{1}{\sec^{2}(x)}dx
integral from 0 to 1 of sin(2pix)	\int\:_{0}^{1}\sin(2πx)dx
limit as x approaches 0 of 0.99^2+1	\lim\:_{x\to\:0}(0.99^{2}+1)
integral of (e^x+9)/((e^x-3)^2)	\int\:\frac{e^{x}+9}{(e^{x}-3)^{2}}dx
(\partial}{\partial x}(\frac{v^2)/x)	\frac{\partial\:}{\partial\:x}(\frac{v^{2}}{x})
integral of-ln(x)e^{-x}	\int\:-\ln(x)e^{-x}dx
tangent of f(x)=4xe^x,\at x=0	tangent\:f(x)=4xe^{x},\at\:x=0
integral of (x^5-x^4+4x^3-4x^2+8x-4)/((x^2+2)^3)	\int\:\frac{x^{5}-x^{4}+4x^{3}-4x^{2}+8x-4}{(x^{2}+2)^{3}}dx
derivative of-(6x)/((x^2-4)^2)	derivative\:-\frac{6x}{(x^{2}-4)^{2}}
integral of ln(x-sqrt(1+x^2))	\int\:\ln(x-\sqrt{1+x^{2}})dx
(\partial)/(\partial x)(xarctan(y))	\frac{\partial\:}{\partial\:x}(x\arctan(y))
sum from n=3 to infinity of (9/11)^{-n}	\sum\:_{n=3}^{\infty\:}(\frac{9}{11})^{-n}
integral of cos^5(4-x)sin(4-x)	\int\:\cos^{5}(4-x)\sin(4-x)dx
integral of (x^2-3x+sqrt(x))/(x^2)	\int\:\frac{x^{2}-3x+\sqrt{x}}{x^{2}}dx
derivative of-6/((x-1^4))	\frac{d}{dx}(-\frac{6}{(x-1)^{4}})
integral of e^{x-2x}sin(x)	\int\:e^{x-2x}\sin(x)dx
y^{''}+4y^'+4y=x^2+e^{-2x}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=x^{2}+e^{-2x}
integral from 0 to 4 of 1/((x-4)^2)	\int\:_{0}^{4}\frac{1}{(x-4)^{2}}dx
integral of (4-ln(x+3))/(x+3)	\int\:\frac{4-\ln(x+3)}{x+3}dx
d/(dy)(4xy)	\frac{d}{dy}(4xy)

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