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Popular Calculus Problems

tangent of f(x)=sqrt(x-1),(17,4)	tangent\:f(x)=\sqrt{x-1},(17,4)
sum from n=0 to infinity of 4-sin(n)	\sum\:_{n=0}^{\infty\:}4-\sin(n)
integral from 0 to 2 of 1/(e^{pix)}	\int\:_{0}^{2}\frac{1}{e^{πx}}dx
(dy)/(dx)+4y=e^{-4x}	\frac{dy}{dx}+4y=e^{-4x}
(\partial)/(\partial x)(3x^2-3)	\frac{\partial\:}{\partial\:x}(3x^{2}-3)
derivative of a^2arcsin(x/a)	\frac{d}{dx}(a^{2}\arcsin(\frac{x}{a}))
integral of (x-1)/(x^2(x+1)^2)	\int\:\frac{x-1}{x^{2}(x+1)^{2}}dx
y^2dy+x^3dx=0	y^{2}dy+x^{3}dx=0
tangent of f(x)= 7/(x^2)-6x^2,\at x=5	tangent\:f(x)=\frac{7}{x^{2}}-6x^{2},\at\:x=5
derivative of sqrt(2x^2+1)	\frac{d}{dx}(\sqrt{2x^{2}+1})
integral of ((1-x))/(e^x)k	\int\:\frac{(1-x)}{e^{x}}kdx
limit as x approaches 0 of+(ln(x))	\lim\:_{x\to\:0}(+(\ln(x)))
y^{''}-8y^'-15y=0	y^{\prime\:\prime\:}-8y^{\prime\:}-15y=0
derivative of (2x)/5	derivative\:\frac{2x}{5}
limit as x approaches 2 of 3x^2+4x-3	\lim\:_{x\to\:2}(3x^{2}+4x-3)
integral of 2(1+2x)^4	\int\:2(1+2x)^{4}dx
integral of (6/(x^4))	\int\:(\frac{6}{x^{4}})dx
derivative of e^{2x}2	\frac{d}{dx}(e^{2x}2)
(\partial)/(\partial x)(xycos(yz))	\frac{\partial\:}{\partial\:x}(xy\cos(yz))
derivative of ln((x^2-1/(x^2+1)))	\frac{d}{dx}(\ln(\frac{x^{2}-1}{x^{2}+1}))
derivative of (x+1/(\sqrt[3]{x})^2)	\frac{d}{dx}((x+\frac{1}{\sqrt[3]{x}})^{2})
derivative of a^2x^2+b^2	derivative\:a^{2}x^{2}+b^{2}
derivative of y=(((x^2+8))/(x^2-8))	derivative\:y=(\frac{(x^{2}+8)}{x^{2}-8})
laplacetransform 3t^2+13t+13	laplacetransform\:3t^{2}+13t+13
maclaurin e^{((x^5))/5}	maclaurin\:e^{\frac{(x^{5})}{5}}
derivative of 1/((1-t^2)^{1/2)}	derivative\:\frac{1}{(1-t^{2})^{\frac{1}{2}}}
tangent of f(x)=((x+1)/(x+3))^2,\at x=-2	tangent\:f(x)=(\frac{x+1}{x+3})^{2},\at\:x=-2
integral from 0 to infinity of ((ye^{-y/a}))/a	\int\:_{0}^{\infty\:}\frac{(ye^{-\frac{y}{a}})}{a}dy
area y=x^2-4x,y=2x+7	area\:y=x^{2}-4x,y=2x+7
(dy)/(dx)=(x^3-y^3)/(3xy^2)	\frac{dy}{dx}=\frac{x^{3}-y^{3}}{3xy^{2}}
integral of 3ln(x^2-x+4)	\int\:3\ln(x^{2}-x+4)dx
((x-2)^2(x+4))^'	((x-2)^{2}(x+4))^{\prime\:}
sum from n=1 to infinity of n/(3^{n^2)}	\sum\:_{n=1}^{\infty\:}\frac{n}{3^{n^{2}}}
f(x)=5x^2e^{3x}	f(x)=5x^{2}e^{3x}
tangent of y=(1+2x)^2,(3,49)	tangent\:y=(1+2x)^{2},(3,49)
inverse oflaplace s/((s+1)^2+4)	inverselaplace\:\frac{s}{(s+1)^{2}+4}
(\partial)/(\partial y)(x^2+y^2+z^2)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}+z^{2})
integral of 5cos^3(2x)	\int\:5\cos^{3}(2x)dx
integral of (ln(x^3))/(-804x^2)	\int\:\frac{\ln(x^{3})}{-804x^{2}}dx
slope of (0.3,-1),(-0.1,-0.8)	slope\:(0.3,-1),(-0.1,-0.8)
(\partial)/(\partial x)(8e^x)	\frac{\partial\:}{\partial\:x}(8e^{x})
derivative of (x^3-2x+1(2x^2+3x))	\frac{d}{dx}((x^{3}-2x+1)(2x^{2}+3x))
tangent of f(x)=(x-6)/(9x-1),\at x=1	tangent\:f(x)=\frac{x-6}{9x-1},\at\:x=1
integral of sqrt(x)+1/(\sqrt[3]{x)}	\int\:\sqrt{x}+\frac{1}{\sqrt[3]{x}}dx
mydx=nxdy	mydx=nxdy
integral from 0 to 1 of 1/(4+x^2)	\int\:_{0}^{1}\frac{1}{4+x^{2}}dx
limit as x approaches 0 of (1/x+1)^x	\lim\:_{x\to\:0}((\frac{1}{x}+1)^{x})
area p(x)=0.7x+20,p(x)=(547.8)/(x+15)	area\:p(x)=0.7x+20,p(x)=\frac{547.8}{x+15}
inverse oflaplace 5/(s^2+3s+2)	inverselaplace\:\frac{5}{s^{2}+3s+2}
limit as x approaches-5 of sqrt((2x^2+7x-15)/(x^2-25))	\lim\:_{x\to\:-5}(\sqrt{\frac{2x^{2}+7x-15}{x^{2}-25}})
(dy)/(dx)=(4sec(y))/((x+3)^2)	\frac{dy}{dx}=\frac{4\sec(y)}{(x+3)^{2}}
integral of 1/(sqrt(4x^2+9))	\int\:\frac{1}{\sqrt{4x^{2}+9}}dx
derivative of f(x)=8sqrt(x)	derivative\:f(x)=8\sqrt{x}
integral of 1/(sqrt(9x^2-1))	\int\:\frac{1}{\sqrt{9x^{2}-1}}dx
(x+y)dx=(y-x)dy	(x+y)dx=(y-x)dy
integral of (21)/((1-x^2)^{3/2)}	\int\:\frac{21}{(1-x^{2})^{\frac{3}{2}}}dx
slope of (-10-6)(-10-5)	slope\:(-10-6)(-10-5)
(dy)/(dt)=sin(y)	\frac{dy}{dt}=\sin(y)
integral of p/(p^2+1)	\int\:\frac{p}{p^{2}+1}dp
integral of (arcsin(x))/(x^2)	\int\:\frac{\arcsin(x)}{x^{2}}dx
(\partial)/(\partial x)(x+2)	\frac{\partial\:}{\partial\:x}(x+2)
area 9x,x^3	area\:9x,x^{3}
integral of u^{-5}(8-u^5+u^{10})	\int\:u^{-5}(8-u^{5}+u^{10})du
limit as n approaches infinity of (n+1)x	\lim\:_{n\to\:\infty\:}((n+1)x)
derivative of (3x-9)/(2x+8)	derivative\:\frac{3x-9}{2x+8}
derivative of t^{-3}	derivative\:t^{-3}
derivative of cos^3((x^2/(1-x)))	\frac{d}{dx}(\cos^{3}(\frac{x^{2}}{1-x}))
limit as x approaches-2 of 1/(sqrt(2-x))	\lim\:_{x\to\:-2}(\frac{1}{\sqrt{2-x}})
derivative of 2sin(x-2xcos(x))	\frac{d}{dx}(2\sin(x)-2x\cos(x))
(\partial)/(\partial x)(ln(1+x^2))	\frac{\partial\:}{\partial\:x}(\ln(1+x^{2}))
tangent of y=4x^2-3x+3,(1,4)	tangent\:y=4x^{2}-3x+3,(1,4)
integral of x^3-3	\int\:x^{3}-3dx
d/(dθ)(e^{tan(θ)})	\frac{d}{dθ}(e^{\tan(θ)})
integral from 0 to 1 of y/(e^{5y)}	\int\:_{0}^{1}\frac{y}{e^{5y}}dy
integral of (2xsqrt(x)-1/(sqrt(x)))	\int\:(2x\sqrt{x}-\frac{1}{\sqrt{x}})dx
3y^{''}-11y^'+10y=0,y(0)=8,y^'(0)=-4	3y^{\prime\:\prime\:}-11y^{\prime\:}+10y=0,y(0)=8,y^{\prime\:}(0)=-4
integral of (e^{4x}-e^{-4x})^2	\int\:(e^{4x}-e^{-4x})^{2}dx
integral of 5/6 csc^2(x/6)	\int\:\frac{5}{6}\csc^{2}(\frac{x}{6})dx
integral of ((2x+3))/(sqrt(x+2))	\int\:\frac{(2x+3)}{\sqrt{x+2}}dx
derivative of f(x)= 2/(3x+1)	derivative\:f(x)=\frac{2}{3x+1}
laplacetransform 5sin(t)	laplacetransform\:5\sin(t)
integral from 0 to 1 of 1/(e^x+1)	\int\:_{0}^{1}\frac{1}{e^{x}+1}dx
ay^'=bx-by	ay^{\prime\:}=bx-by
(dy)/(dx)+(5x)y=3x+5	\frac{dy}{dx}+(5x)y=3x+5
integral of e^t+e^{-t}	\int\:e^{t}+e^{-t}dt
(\partial)/(\partial z)(sin(xy))	\frac{\partial\:}{\partial\:z}(\sin(xy))
(\partial)/(\partial y)(ln((y^9)/(x^7)))	\frac{\partial\:}{\partial\:y}(\ln(\frac{y^{9}}{x^{7}}))
integral from 0 to 60 of 25e^{-0.03x}	\int\:_{0}^{60}25e^{-0.03x}dx
integral of (9t-4)/(t+1)	\int\:\frac{9t-4}{t+1}dt
d/(d{x)}({x}{y}{z}+5/4 {z}^4+e^{{x}}cos({y}))	\frac{d}{d{x}}({x}{y}{z}+\frac{5}{4}{z}^{4}+e^{{x}}\cos({y}))
limit as x approaches 0 of xsin(3/x)	\lim\:_{x\to\:0}(x\sin(\frac{3}{x}))
integral of sin^2(o)	\int\:\sin^{2}(o)do
inverse oflaplace ((s+3)^2)/(s(s^2+10))	inverselaplace\:\frac{(s+3)^{2}}{s(s^{2}+10)}
integral of 1x^2	\int\:1x^{2}dx
derivative of 15x^2	\frac{d}{dx}(15x^{2})
integral of ((x-1)^2)/x	\int\:\frac{(x-1)^{2}}{x}dx
integral from 0 to 1 of (89)/(x^5)	\int\:_{0}^{1}\frac{89}{x^{5}}dx
xy^'+2y=x^3-4	xy^{\prime\:}+2y=x^{3}-4
integral from 4 to infinity of 7e^{-x/2}	\int\:_{4}^{\infty\:}7e^{-\frac{x}{2}}dx
derivative of 4^{-x^2}	\frac{d}{dx}(4^{-x^{2}})

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