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Popular Calculus Problems

integral from 7 to 14 of 1/((x-9)^2)	\int\:_{7}^{14}\frac{1}{(x-9)^{2}}dx
integral from 0 to 4 of \|3t-8\|	\int\:_{0}^{4}\left\|3t-8\right\|dt
derivative of f(x)=(4x^2-x+3)/(sqrt(x))	derivative\:f(x)=\frac{4x^{2}-x+3}{\sqrt{x}}
integral of (e^{-st})/(-s)	\int\:\frac{e^{-st}}{-s}dt
inverse oflaplace (s^4+10)/(s-2)	inverselaplace\:\frac{s^{4}+10}{s-2}
(\partial)/(\partial x)(6x^2+5x^3y^4-10y^5)	\frac{\partial\:}{\partial\:x}(6x^{2}+5x^{3}y^{4}-10y^{5})
integral of 3/(x^2sqrt(x^2-9))	\int\:\frac{3}{x^{2}\sqrt{x^{2}-9}}dx
integral of (x+2)/(2x-1)	\int\:\frac{x+2}{2x-1}dx
area y=e^{3x},y=e^{4x},x=1	area\:y=e^{3x},y=e^{4x},x=1
area x=7-7y^2,x=7y^2-7	area\:x=7-7y^{2},x=7y^{2}-7
2ty^2dt+2t^2ydy=0	2ty^{2}dt+2t^{2}ydy=0
integral of (e^{cos(x)}sin(x))	\int\:(e^{\cos(x)}\sin(x))dx
limit as x approaches 0 of ln(x^2)2e^x+1	\lim\:_{x\to\:0}(\ln(x^{2})2e^{x}+1)
derivative of cos^{sin(x}(x))	\frac{d}{dx}(\cos^{\sin(x)}(x))
integral of (r^4)/(sqrt(4+r^2))	\int\:\frac{r^{4}}{\sqrt{4+r^{2}}}dr
derivative of tan(4x^2)	\frac{d}{dx}(\tan(4x^{2}))
integral from 0 to 1 of (x-5)/(x^2-5x+6)	\int\:_{0}^{1}\frac{x-5}{x^{2}-5x+6}dx
derivative of (2x-5)^4(x^2+x+1)^5	derivative\:(2x-5)^{4}(x^{2}+x+1)^{5}
derivative of (log_{e}(x)/x)	\frac{d}{dx}(\frac{\log_{e}(x)}{x})
derivative of sin(x^2+3x)	\frac{d}{dx}(\sin(x^{2}+3x))
integral of (-x^2-9x-1)/(x+8)	\int\:\frac{-x^{2}-9x-1}{x+8}dx
integral of e^{-x/7}	\int\:e^{-\frac{x}{7}}dx
derivative of x^{3/5}	derivative\:x^{\frac{3}{5}}
(\partial)/(\partial x)((2x-3y)/(2x+3y))	\frac{\partial\:}{\partial\:x}(\frac{2x-3y}{2x+3y})
integral of 3x^5sqrt(x^3+1)	\int\:3x^{5}\sqrt{x^{3}+1}dx
integral of (arcsin(6x))/(sqrt(1-36x^2))	\int\:\frac{\arcsin(6x)}{\sqrt{1-36x^{2}}}dx
derivative of y=x^{1/x}	derivative\:y=x^{\frac{1}{x}}
integral of e^{-4x}sin(x)	\int\:e^{-4x}\sin(x)dx
(\partial)/(\partial x)((2x)/(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(\frac{2x}{x^{2}+y^{2}+z^{2}})
integral from 0 to 4 of xe^{-0.1x}	\int\:_{0}^{4}xe^{-0.1x}dx
derivative of ln^2(x-1)	\frac{d}{dx}(\ln^{2}(x-1))
limit as x approaches+0 of ((1+x)^4-1)/x	\lim\:_{x\to\:+0}(\frac{(1+x)^{4}-1}{x})
integral of 1/2 cos^2(x)	\int\:\frac{1}{2}\cos^{2}(x)dx
(\partial)/(\partial y)(xy+yz+zx)	\frac{\partial\:}{\partial\:y}(xy+yz+zx)
integral of (x^4-3x^2+7)/(x^4)	\int\:\frac{x^{4}-3x^{2}+7}{x^{4}}dx
limit as x approaches 5 of (f(x))/(g(x))	\lim\:_{x\to\:5}(\frac{f(x)}{g(x)})
(\partial)/(\partial x)(3x-y)	\frac{\partial\:}{\partial\:x}(3x-y)
integral of sin(n)x	\int\:\sin(n)xdx
integral from 0 to 2 of 6-x^2	\int\:_{0}^{2}6-x^{2}dx
(\partial)/(\partial y)(sqrt(2x+3y))	\frac{\partial\:}{\partial\:y}(\sqrt{2x+3y})
tangent of x^2+2x+3	tangent\:x^{2}+2x+3
derivative of ((-1^x)/x)	\frac{d}{dx}(\frac{(-1)^{x}}{x})
18y^'=y^3-9y	18y^{\prime\:}=y^{3}-9y
limit as x approaches 2 of 1-x^2	\lim\:_{x\to\:2}(1-x^{2})
area y=4sqrt(x),y=(4x)/3	area\:y=4\sqrt{x},y=\frac{4x}{3}
y^'=1-t+y-ty	y^{\prime\:}=1-t+y-ty
integral of (ln^3(x^2))/x	\int\:\frac{\ln^{3}(x^{2})}{x}dx
derivative of (6x)/(4+x^2)	derivative\:\frac{6x}{4+x^{2}}
(\partial)/(\partial x)(cos(6x))	\frac{\partial\:}{\partial\:x}(\cos(6x))
derivative of \|x^3+8x^2+5x-50\|	\frac{d}{dx}(\left\|x^{3}+8x^{2}+5x-50\right\|)
integral of 1/(2+8x)	\int\:\frac{1}{2+8x}dx
integral of sec(13w)tan(13w)	\int\:\sec(13w)\tan(13w)dw
integral from 0 to pi/4 of tan^3(x)	\int\:_{0}^{\frac{π}{4}}\tan^{3}(x)dx
(2y^2x+3x^2)dx+2x^2ydy=0	(2y^{2}x+3x^{2})dx+2x^{2}ydy=0
derivative of (x^3/(x+2))	\frac{d}{dx}(\frac{x^{3}}{x+2})
x^9y^'-9x^8y=5y^2	x^{9}y^{\prime\:}-9x^{8}y=5y^{2}
d/(dt)(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t))	\frac{d}{dt}(t-2(t-1)u_{(1)}(t)+(t-2){u_{(2)}}(t)(t))
laplacetransform sin(4t)cos(3t)	laplacetransform\:\sin(4t)\cos(3t)
derivative of (1+2x^{1/2})	\frac{d}{dx}((1+2x)^{\frac{1}{2}})
laplacetransform t+3	laplacetransform\:t+3
integral of 10x-3	\int\:10x-3dx
area y= 1/x ,y=x,y= x/4	area\:y=\frac{1}{x},y=x,y=\frac{x}{4}
(dy)/(dx)=1-cos(2x-y+3)	\frac{dy}{dx}=1-\cos(2x-y+3)
derivative of f(x)= 8/(x^3)	derivative\:f(x)=\frac{8}{x^{3}}
inverse oflaplace 5/(s^2(s+2))	inverselaplace\:\frac{5}{s^{2}(s+2)}
integral from 0 to 1 of xcos((npix)/2)	\int\:_{0}^{1}x\cos(\frac{nπx}{2})dx
derivative of ln(1/(2x+3))	derivative\:\ln(\frac{1}{2x+3})
inverse oflaplace 1/((5*s+1))	inverselaplace\:\frac{1}{(5\cdot\:s+1)}
derivative of (x+1^4)	\frac{d}{dx}((x+1)^{4})
derivative of (ax/(x^2+a^2))	\frac{d}{dx}(\frac{ax}{x^{2}+a^{2}})
integral of (x^4+2sqrt(x)-16)	\int\:(x^{4}+2\sqrt{x}-16)dx
derivative of e^{sqrt(x^3)}	\frac{d}{dx}(e^{\sqrt{x^{3}}})
derivative of a(1-cos(x))	\frac{d}{dx}(a(1-\cos(x)))
(\partial)/(\partial x)(e^{2y^2}+4x^2)	\frac{\partial\:}{\partial\:x}(e^{2y^{2}}+4x^{2})
integral from 1 to 5 of 1/((x-4)^2)	\int\:_{1}^{5}\frac{1}{(x-4)^{2}}dx
integral of-2xcos(3x)	\int\:-2x\cos(3x)dx
derivative of (x^2-2x^{sin(x)})	\frac{d}{dx}((x^{2}-2x)^{\sin(x)})
y^'+3y=x+e^{-2x}	y^{\prime\:}+3y=x+e^{-2x}
limit as x approaches infinity of x-2^x	\lim\:_{x\to\:\infty\:}(x-2^{x})
y^{''}+8y^'+9y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+9y=0
integral of x^2(2-x)	\int\:x^{2}(2-x)dx
limit as x approaches 1 of ln(1)	\lim\:_{x\to\:1}(\ln(1))
derivative of \sqrt[3]{6x^2+7x+2}	\frac{d}{dx}(\sqrt[3]{6x^{2}+7x+2})
limit as x approaches 0 of 5-(\|x\|)/x	\lim\:_{x\to\:0}(5-\frac{\left\|x\right\|}{x})
integral from-pi to pi of cos(x)	\int\:_{-π}^{π}\cos(x)dx
slope of (-9,-6),(-4,5)	slope\:(-9,-6),(-4,5)
(\partial)/(\partial v)(u^2+v^2-4)	\frac{\partial\:}{\partial\:v}(u^{2}+v^{2}-4)
xy^'+y=-7xy^2,y(1)=-6	xy^{\prime\:}+y=-7xy^{2},y(1)=-6
integral of 14-(20-3sqrt(16-2x))	\int\:14-(20-3\sqrt{16-2x})dx
derivative of y^{-1}	derivative\:y^{-1}
(\partial)/(\partial y)(1/(y^2))	\frac{\partial\:}{\partial\:y}(\frac{1}{y^{2}})
(dy)/(dx)=12-y	\frac{dy}{dx}=12-y
derivative of x^{-3}	derivative\:x^{-3}
integral of-pi+2tcos(n)t	\int\:-π+2t\cos(n)tdt
sum from n=1 to infinity of e^n	\sum\:_{n=1}^{\infty\:}e^{n}
integral of 4/(x^2+4)	\int\:\frac{4}{x^{2}+4}dx
integral of ((csc^2(x))/(cot^3(x)))	\int\:(\frac{\csc^{2}(x)}{\cot^{3}(x)})dx
integral of tan^2(pi/4 x)	\int\:\tan^{2}(\frac{π}{4}x)dx
(dQ)/(dt)=k(Q-70)	\frac{dQ}{dt}=k(Q-70)
derivative of-3/2 x^3+2/5 x^2-4	\frac{d}{dx}(-\frac{3}{2}x^{3}+\frac{2}{5}x^{2}-4)

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