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Popular Calculus Problems

integral of (x^2)/(25+x^2)	\int\:\frac{x^{2}}{25+x^{2}}dx
derivative of 3\sqrt[3]{x^4}	\frac{d}{dx}(3\sqrt[3]{x^{4}})
(\partial)/(\partial x)(4y(1/x-ln(x)))	\frac{\partial\:}{\partial\:x}(4y(\frac{1}{x}-\ln(x)))
integral from 0 to pi of xsin(2x)	\int\:_{0}^{π}x\sin(2x)dx
(\partial)/(\partial x)(xe^{sqrt(15xy)})	\frac{\partial\:}{\partial\:x}(xe^{\sqrt{15xy}})
(\partial)/(\partial x)(-y+x+2)	\frac{\partial\:}{\partial\:x}(-y+x+2)
sum from n=3 to infinity}((-1)^{n+1 of)/(n!)	\sum\:_{n=3}^{\infty\:}\frac{(-1)^{n+1}}{n!}
integral of e^{(x^2)}	\int\:e^{(x^{2})}dx
integral of 3e^{x^2}x	\int\:3e^{x^{2}}xdx
limit as x approaches 0+of (7x)/(\|x\|)	\lim\:_{x\to\:0+}(\frac{7x}{\left\|x\right\|})
t^2(dy)/(dt)+ty=5	t^{2}\frac{dy}{dt}+ty=5
integral of sqrt(3x+4)	\int\:\sqrt{3x+4}dx
integral of cos(u)sin(u)	\int\:\cos(u)\sin(u)du
(\partial)/(\partial y)(6xy^3)	\frac{\partial\:}{\partial\:y}(6xy^{3})
derivative of ((x+1)/x)	\frac{d}{dx}(\frac{(x+1)}{x})
derivative of arcsin(4x)	derivative\:\arcsin(4x)
integral of (x^3)/(y^2)	\int\:\frac{x^{3}}{y^{2}}dx
taylor 1/((x+1)^2)1	taylor\:\frac{1}{(x+1)^{2}}1
integral of x^2sqrt(9+x^2)	\int\:x^{2}\sqrt{9+x^{2}}dx
inverse oflaplace 1/(2002s^2+9)	inverselaplace\:\frac{1}{2002s^{2}+9}
y^'=(x^3y^3+4x^3)/(y^2)	y^{\prime\:}=\frac{x^{3}y^{3}+4x^{3}}{y^{2}}
derivative of x^2+y^2=25	\frac{d}{dx}(x^{2}+y^{2})=25
(\partial)/(\partial x)(9x^2)	\frac{\partial\:}{\partial\:x}(9x^{2})
derivative of f(x)=4-x^2	derivative\:f(x)=4-x^{2}
limit as x approaches-2 of (x^2-1)/(2-x)	\lim\:_{x\to\:-2}(\frac{x^{2}-1}{2-x})
tangent of y=sqrt(x),(25,5)	tangent\:y=\sqrt{x},(25,5)
(d^2)/(dx^2)((x^2-1)/(x^2+1))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}-1}{x^{2}+1})
derivative of 1/pi cx^2+ln(cos^3(x))	\frac{d}{dx}(\frac{1}{π}cx^{2}+\ln(\cos^{3}(x)))
integral from 1 to 9 of 1/(6-sqrt(x))	\int\:_{1}^{9}\frac{1}{6-\sqrt{x}}dx
area \sqrt[3]{x},(x-1)^2	area\:\sqrt[3]{x},(x-1)^{2}
integral of 1/x sqrt(1+x^2)	\int\:\frac{1}{x}\sqrt{1+x^{2}}dx
tangent of f(x)=x^3-2x+2,(2,6)	tangent\:f(x)=x^{3}-2x+2,(2,6)
4t(dy)/(dt)-3y=sqrt(t)	4t\frac{dy}{dt}-3y=\sqrt{t}
derivative of-2xsin(2x+cos(2x))	\frac{d}{dx}(-2x\sin(2x)+\cos(2x))
inverse oflaplace ((s+1))/(s(s^2+s+1))	inverselaplace\:\frac{(s+1)}{s(s^{2}+s+1)}
(dy)/(dx)+1=2y	\frac{dy}{dx}+1=2y
integral of e^r	\int\:e^{r}dr
integral of (15x^{-1}-4sinh(x))	\int\:(15x^{-1}-4\sinh(x))dx
derivative of (x^6+1^{5/2})	\frac{d}{dx}((x^{6}+1)^{\frac{5}{2}})
integral of tan^3(x)sec^4(x)	\int\:\tan^{3}(x)\sec^{4}(x)dx
laplacetransform t^{3/2}*e^{-2t}	laplacetransform\:t^{\frac{3}{2}}\cdot\:e^{-2t}
(\partial)/(\partial s)(t/s)	\frac{\partial\:}{\partial\:s}(\frac{t}{s})
integral from 0 to 1 of (x^3)/(x^2+1)	\int\:_{0}^{1}\frac{x^{3}}{x^{2}+1}dx
integral of 1/5 x	\int\:\frac{1}{5}xdx
integral of 2/(x^3sqrt(x^4-81))	\int\:\frac{2}{x^{3}\sqrt{x^{4}-81}}dx
d/(dt)(e^{-at}cos(wt))	\frac{d}{dt}(e^{-at}\cos(wt))
integral of (x^22^x+x)/(x^2)	\int\:\frac{x^{2}2^{x}+x}{x^{2}}dx
derivative of ((3x^2+1^3)/((2x^2-1)^4))	\frac{d}{dx}(\frac{(3x^{2}+1)^{3}}{(2x^{2}-1)^{4}})
f^'(x)=a^{2x}	f^{\prime\:}(x)=a^{2x}
sum from n=1 to infinity of ((n-2)/n)^n	\sum\:_{n=1}^{\infty\:}(\frac{n-2}{n})^{n}
integral of (sin(2u)-cos(3u))^{(2)}	\int\:(\sin(2u)-\cos(3u))^{(2)}du
derivative of sqrt(-3x-9)	\frac{d}{dx}(\sqrt{-3x-9})
integral of y/((1+y^2)^4)	\int\:\frac{y}{(1+y^{2})^{4}}dy
derivative of [x+(x+sin^2(x))^3]^4	derivative\:[x+(x+\sin^{2}(x))^{3}]^{4}
limit as x approaches 2+of (x^2-4)/(x-2)	\lim\:_{x\to\:2+}(\frac{x^{2}-4}{x-2})
integral of tan^5(4x)sec^4(4x)	\int\:\tan^{5}(4x)\sec^{4}(4x)dx
limit as x approaches-infinity of-x^2	\lim\:_{x\to\:-\infty\:}(-x^{2})
inverse oflaplace 1/((s^2-2s+5))	inverselaplace\:\frac{1}{(s^{2}-2s+5)}
tangent of f(x)=sqrt(25-x),\at x=0	tangent\:f(x)=\sqrt{25-x},\at\:x=0
integral of (3^{-x})	\int\:(3^{-x})dx
implicit (dy)/(dx),y=x^2+3	implicit\:\frac{dy}{dx},y=x^{2}+3
derivative of xsin(pi/x)	\frac{d}{dx}(x\sin(\frac{π}{x}))
f(x)=tan(ln(x))	f(x)=\tan(\ln(x))
integral from-3 to 5 of (2y-(y^2-15))	\int\:_{-3}^{5}(2y-(y^{2}-15))dy
derivative of 2x^{3/2}	derivative\:2x^{\frac{3}{2}}
y^'=((y-y^2)t)/(1+t^2)	y^{\prime\:}=\frac{(y-y^{2})t}{1+t^{2}}
integral of 2xsin(2x)	\int\:2x\sin(2x)dx
integral of-kxe^{-kx}	\int\:-kxe^{-kx}dx
(\partial)/(\partial x)(cos(x+y))	\frac{\partial\:}{\partial\:x}(\cos(x+y))
integral of (2x-1)	\int\:(2x-1)dx
derivative of-3/(sqrt(x))	derivative\:-\frac{3}{\sqrt{x}}
derivative of acos^2(x)	\frac{d}{dx}(a\cos^{2}(x))
sum from n=0 to infinity of 4	\sum\:_{n=0}^{\infty\:}4
(\partial)/(\partial x)((x^2+y^2)^3)	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{3})
(\partial)/(\partial x)(f(x,y)x(x,y))	\frac{\partial\:}{\partial\:x}(f(x,y)x(x,y))
(dy)/(dx)=8y	\frac{dy}{dx}=8y
tangent of f(x)=(2/(x-2)),\at x=4	tangent\:f(x)=(\frac{2}{x-2}),\at\:x=4
integral from 0 to ln(3) of 3/(e^x+2)	\int\:_{0}^{\ln(3)}\frac{3}{e^{x}+2}dx
(x-2)(dy)/(dx)-y=3	(x-2)\frac{dy}{dx}-y=3
tangent of y=9x-8sqrt(x),(1,1)	tangent\:y=9x-8\sqrt{x},(1,1)
derivative of ((2-z)^{2/3})/(4z+5)	derivative\:\frac{(2-z)^{\frac{2}{3}}}{4z+5}
derivative of (3x+2^4)	\frac{d}{dx}((3x+2)^{4})
derivative of f(x)=28x^2-10x-2	derivative\:f(x)=28x^{2}-10x-2
(dy)/(dx)=sin(y)ln(x)	\frac{dy}{dx}=\sin(y)\ln(x)
integral of (2x)/(x^2+4x+4)	\int\:\frac{2x}{x^{2}+4x+4}dx
integral from-infinity to-2 of xe^x	\int\:_{-\infty\:}^{-2}xe^{x}dx
integral from 0 to 4 of 3/64 x^2	\int\:_{0}^{4}\frac{3}{64}x^{2}dx
1/4 y^{''}+4y=2tan(4t)	\frac{1}{4}y^{\prime\:\prime\:}+4y=2\tan(4t)
limit as x approaches 6-of ln(x-6)	\lim\:_{x\to\:6-}(\ln(x-6))
derivative of sqrt(sin(1+x^2))	derivative\:\sqrt{\sin(1+x^{2})}
derivative of sec^3(4x)	\frac{d}{dx}(\sec^{3}(4x))
laplacetransform cos(t+pi/5)	laplacetransform\:\cos(t+\frac{π}{5})
integral of cos(4t)-sin(4t)	\int\:\cos(4t)-\sin(4t)dt
integral of (x^2)/(2(x+1))	\int\:\frac{x^{2}}{2(x+1)}dx
derivative of e^{9x^2}	\frac{d}{dx}(e^{9x^{2}})
x^{''}+2x=0	x^{\prime\:\prime\:}+2x=0
derivative of y=x^3-3x+1	derivative\:y=x^{3}-3x+1
(\partial)/(\partial x)(sin(x)+x^2e^y-1)	\frac{\partial\:}{\partial\:x}(\sin(x)+x^{2}e^{y}-1)
derivative of f(x)=(ln(x))/(x^3)	derivative\:f(x)=\frac{\ln(x)}{x^{3}}
limit as x approaches 0.01 of ax^2-x+b	\lim\:_{x\to\:0.01}(ax^{2}-x+b)

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