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Popular Calculus Problems

integral of (6(1+x))/(x(x^2+7x+6))	\int\:\frac{6(1+x)}{x(x^{2}+7x+6)}dx
(\partial)/(\partial x)(cos^4(x^3y^5))	\frac{\partial\:}{\partial\:x}(\cos^{4}(x^{3}y^{5}))
limit as x approaches-8 of x^2-3	\lim\:_{x\to\:-8}(x^{2}-3)
derivative of f(x)=4x^3-8x	derivative\:f(x)=4x^{3}-8x
derivative of ae^{bt}	derivative\:ae^{bt}
tangent of f(x)= 3/(x+2),\at x=3	tangent\:f(x)=\frac{3}{x+2},\at\:x=3
derivative of sin(9x)+cos(2x)	derivative\:\sin(9x)+\cos(2x)
integral of (1-z)/(-1-z)	\int\:\frac{1-z}{-1-z}
(ln(sqrt(x)))^'	(\ln(\sqrt{x}))^{\prime\:}
integral of (x^2-2x-3)	\int\:(x^{2}-2x-3)dx
(x^2+1)y^'+y^2+1=0,y(4)=e	(x^{2}+1)y^{\prime\:}+y^{2}+1=0,y(4)=e
integral of 1/((sin(x))^2(cos(x))^4)	\int\:\frac{1}{(\sin(x))^{2}(\cos(x))^{4}}dx
(d^4)/(dx^4)(ln(x))	\frac{d^{4}}{dx^{4}}(\ln(x))
integral from 1 to infinity of 1/(\sqrt[3]{x)}	\int\:_{1}^{\infty\:}\frac{1}{\sqrt[3]{x}}dx
derivative of 15x^{1/4}	derivative\:15x^{\frac{1}{4}}
sum from n=0 to infinity of (2/3)^{n-1}	\sum\:_{n=0}^{\infty\:}(\frac{2}{3})^{n-1}
y^'=(xy^3)/(25),y(0)=10	y^{\prime\:}=\frac{xy^{3}}{25},y(0)=10
9y^{''}-18y^'+15y=0	9y^{\prime\:\prime\:}-18y^{\prime\:}+15y=0
limit as x approaches 0 of (sqrt(x^2+p^2)-p)/(sqrt(x^2+q(x)^2)-q(x))	\lim\:_{x\to\:0}(\frac{\sqrt{x^{2}+p^{2}}-p}{\sqrt{x^{2}+q(x)^{2}}-q(x)})
derivative of 3sin(x)	derivative\:3\sin(x)
tangent of 2/(4-x)	tangent\:\frac{2}{4-x}
integral of-2t	\int\:-2tdt
integral of (sec^2(x))/(tan^5(x))	\int\:\frac{\sec^{2}(x)}{\tan^{5}(x)}dx
integral of 1/(sec^3(y))	\int\:\frac{1}{\sec^{3}(y)}dy
f(θ)=θcos(θ)	f(θ)=θ\cos(θ)
integral from 0 to 6 of x^2	\int\:_{0}^{6}x^{2}dx
derivative of sec(x)-sqrt(22)tan(x)	derivative\:\sec(x)-\sqrt{22}\tan(x)
(\partial)/(\partial x)(4y^2e^{7x})	\frac{\partial\:}{\partial\:x}(4y^{2}e^{7x})
y=(8e^{8x})/(7x+2)	y=\frac{8e^{8x}}{7x+2}
integral of e^xsqrt(2-e^x)	\int\:e^{x}\sqrt{2-e^{x}}dx
(\partial)/(\partial y)(x^2yz^3)	\frac{\partial\:}{\partial\:y}(x^{2}yz^{3})
derivative of f(x)=sqrt(1-4x)	derivative\:f(x)=\sqrt{1-4x}
derivative of 4/((1+2x^2))	\frac{d}{dx}(\frac{4}{(1+2x)^{2}})
derivative of ln(17x)	\frac{d}{dx}(\ln(17x))
limit as x approaches-5 of 3x-\|x+5\|	\lim\:_{x\to\:-5}(3x-\left\|x+5\right\|)
slope of y= 1/(x-2),\at x=5	slope\:y=\frac{1}{x-2},\at\:x=5
integral from 0 to 3 of ln(x+1)	\int\:_{0}^{3}\ln(x+1)dx
integral of (1-x)^n	\int\:(1-x)^{n}dx
sum from n=0 to infinity of e^{-5n}	\sum\:_{n=0}^{\infty\:}e^{-5n}
integral from 0 to 2 of 0.09375(4-x^2)	\int\:_{0}^{2}0.09375(4-x^{2})dx
integral of sec(6w)tan(6w)	\int\:\sec(6w)\tan(6w)dw
integral of 2sqrt(x)-x	\int\:2\sqrt{x}-xdx
tangent of y=sqrt(x+5),\at x=11	tangent\:y=\sqrt{x+5},\at\:x=11
derivative of (8(4^x))/(x^4)	derivative\:\frac{8(4^{x})}{x^{4}}
integral from-1 to 4 of \|x-2x^2\|	\int\:_{-1}^{4}\left\|x-2x^{2}\right\|dx
(\partial)/(\partial x)(xye^y)	\frac{\partial\:}{\partial\:x}(xye^{y})
f(x)=2^{sin(x)}	f(x)=2^{\sin(x)}
derivative of y=(8/x)^{5x}	derivative\:y=(\frac{8}{x})^{5x}
derivative of ln(x+sqrt(x^2+5))	\frac{d}{dx}(\ln(x+\sqrt{x^{2}+5}))
integral from 1 to 3 of 1/(x^2-2x+5)	\int\:_{1}^{3}\frac{1}{x^{2}-2x+5}dx
integral of e^{i7x}cos(4x)	\int\:e^{i7x}\cos(4x)dx
integral of e^{2x}x^3	\int\:e^{2x}x^{3}dx
inverse oflaplace ((s-1))/(4s^2+s+24)	inverselaplace\:\frac{(s-1)}{4s^{2}+s+24}
derivative of (2x^3-3x^2/((x-1)^2))	\frac{d}{dx}(\frac{2x^{3}-3x^{2}}{(x-1)^{2}})
y^'=(4t^3+1)/(2y-6),y(1)=2	y^{\prime\:}=\frac{4t^{3}+1}{2y-6},y(1)=2
integral of (e^{6/t})/(t^2)	\int\:\frac{e^{\frac{6}{t}}}{t^{2}}dt
(\partial)/(\partial x)(x/(x^2+y^2)-3xz)	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+y^{2}}-3xz)
derivative of x^2+x+2	\frac{d}{dx}(x^{2}+x+2)
implicit (dy)/(dx),2x^2+y^2-7=0	implicit\:\frac{dy}{dx},2x^{2}+y^{2}-7=0
derivative of f(x)=\sqrt[4]{x^5}	derivative\:f(x)=\sqrt[4]{x^{5}}
integral of 1/(x^2+2x+26)	\int\:\frac{1}{x^{2}+2x+26}dx
slope ofintercept (-12,0),(-15,-3)	slopeintercept\:(-12,0),(-15,-3)
(dy)/(dx)=-2xy	\frac{dy}{dx}=-2xy
derivative of 3x^{2/3}-2x	derivative\:3x^{\frac{2}{3}}-2x
inverse oflaplace s/(s+10^4)	inverselaplace\:\frac{s}{s+10^{4}}
integral of 6x^{3/5}	\int\:6x^{\frac{3}{5}}dx
integral from 1 to e^2 of (ln^7(x^2))/x	\int\:_{1}^{e^{2}}\frac{\ln^{7}(x^{2})}{x}dx
derivative of x-sin(x)	\frac{d}{dx}(x-\sin(x))
derivative of arctan(5x)	derivative\:\arctan(5x)
(dy)/(dx)=x-x^2	\frac{dy}{dx}=x-x^{2}
derivative of f(x)=sin(x)+cos(x)	derivative\:f(x)=\sin(x)+\cos(x)
integral of sin^4(3x)	\int\:\sin^{4}(3x)dx
derivative of Ae^{-4}	derivative\:Ae^{-4}
integral of x/(x^2+x-6)	\int\:\frac{x}{x^{2}+x-6}dx
inverse oflaplace 2/(3(s+1)^2-27)	inverselaplace\:\frac{2}{3(s+1)^{2}-27}
integral of (x+5)/(sqrt(x^2+9))	\int\:\frac{x+5}{\sqrt{x^{2}+9}}dx
integral of (x-1)/((x-2)(x-3))	\int\:\frac{x-1}{(x-2)(x-3)}dx
y^'+e^xy=7e^x	y^{\prime\:}+e^{x}y=7e^{x}
derivative of (7x+1)(x^2-6)	derivative\:(7x+1)(x^{2}-6)
d/(dy)(sqrt(a^2-y^2))	\frac{d}{dy}(\sqrt{a^{2}-y^{2}})
integral of cos^3(2x)sin^5(2x)	\int\:\cos^{3}(2x)\sin^{5}(2x)dx
integral of (5x)/(x^2+4)	\int\:\frac{5x}{x^{2}+4}dx
(\partial)/(\partial x)(5xsin(xy))	\frac{\partial\:}{\partial\:x}(5x\sin(xy))
(\partial)/(\partial x)(ln(8ye^{xy}))	\frac{\partial\:}{\partial\:x}(\ln(8ye^{xy}))
integral of 1/((25-x^2)^2)	\int\:\frac{1}{(25-x^{2})^{2}}dx
tangent of 3x^2-x^3	tangent\:3x^{2}-x^{3}
(\partial)/(\partial x)(3sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(3\sqrt{x^{2}+y^{2}})
integral from x to 3 of sin(t^2)	\int\:_{x}^{3}\sin(t^{2})dt
derivative of (50/(x^7))	\frac{d}{dx}(\frac{50}{x^{7}})
(dy)/(dx)(xsqrt(16-x))=0	\frac{dy}{dx}(x\sqrt{16-x})=0
laplacetransform 4e^{-7t}cos(9t)	laplacetransform\:4e^{-7t}\cos(9t)
integral of \sqrt[4]{e^x}	\int\:\sqrt[4]{e^{x}}dx
integral from-infinity to 0 of 1/(2-9x)	\int\:_{-\infty\:}^{0}\frac{1}{2-9x}dx
derivative of sqrt(3x^2+9x+2)	\frac{d}{dx}(\sqrt{3x^{2}+9x+2})
(dy)/(dx)=0	\frac{dy}{dx}=0
integral of (e^{sqrt(x+3)})/(sqrt(x+3))	\int\:\frac{e^{\sqrt{x+3}}}{\sqrt{x+3}}dx
area y=-1/2 x^2+2,y=0	area\:y=-\frac{1}{2}x^{2}+2,y=0
integral of \sqrt[9]{e^x}	\int\:\sqrt[9]{e^{x}}dx
(y^2+1)dx=ysec^2(x)dy	(y^{2}+1)dx=y\sec^{2}(x)dy
limit as x approaches 0 of x^{-2}	\lim\:_{x\to\:0}(x^{-2})

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