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Popular Calculus Problems

integral of 1/(-10sqrt(x)-10x)	\int\:\frac{1}{-10\sqrt{x}-10x}dx
integral of 8/(x(x^2+25))	\int\:\frac{8}{x(x^{2}+25)}dx
derivative of x^2arcsin(x)	\frac{d}{dx}(x^{2}\arcsin(x))
limit as x approaches 0 of y/x	\lim\:_{x\to\:0}(\frac{y}{x})
implicit (dy)/(dx),e^{x/y}=7x-y	implicit\:\frac{dy}{dx},e^{\frac{x}{y}}=7x-y
xy^'-2y=x	xy^{\prime\:}-2y=x
sum from n=0 to infinity of (n2^n)/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{n2^{n}}{3^{n}}
derivative of y=x^3(2x-1)^5	derivative\:y=x^{3}(2x-1)^{5}
(\partial)/(\partial x)((x+y)/(1-xy))	\frac{\partial\:}{\partial\:x}(\frac{x+y}{1-xy})
derivative of f(x)=x^3-3x	derivative\:f(x)=x^{3}-3x
derivative of (x^2-5)(x+7)	derivative\:(x^{2}-5)(x+7)
integral of sin(11x)	\int\:\sin(11x)dx
integral from 0 to 2 of x^2-4	\int\:_{0}^{2}x^{2}-4dx
(\partial)/(\partial y)(3z)	\frac{\partial\:}{\partial\:y}(3z)
derivative of (2sin(x)/(2+cos(x)))	\frac{d}{dx}(\frac{2\sin(x)}{2+\cos(x)})
derivative of (x^2+2x)/(4-5x)	derivative\:\frac{x^{2}+2x}{4-5x}
derivative of f(x)=sin(tan(9x))	derivative\:f(x)=\sin(\tan(9x))
laplacetransform 3e^{-2t}	laplacetransform\:3e^{-2t}
derivative of x/((x-1)^2)	derivative\:\frac{x}{(x-1)^{2}}
integral of (x^2)/(5x^3+2)	\int\:\frac{x^{2}}{5x^{3}+2}dx
(x+1)y^'=xy	(x+1)y^{\prime\:}=xy
derivative of cos(x+cos(2x))	\frac{d}{dx}(\cos(x)+\cos(2x))
area f(x)=x^2-2x+1,(1,4)	area\:f(x)=x^{2}-2x+1,(1,4)
integral of ((2r+1))/((r^2-3r+2))	\int\:\frac{(2r+1)}{(r^{2}-3r+2)}dr
xdy-ydx=0	xdy-ydx=0
tangent of (-2x)/((x^2+1))	tangent\:\frac{-2x}{(x^{2}+1)}
integral of (3x)/4	\int\:\frac{3x}{4}dx
limit as x approaches infinity of x-0	\lim\:_{x\to\:\infty\:}(x-0)
integral from 3 to infinity of 1/(x^4)	\int\:_{3}^{\infty\:}\frac{1}{x^{4}}dx
integral of 1/(x^7)	\int\:\frac{1}{x^{7}}dx
derivative of (x+2)e^{-x}	derivative\:(x+2)e^{-x}
factor 6x^4+8x^3	factor\:6x^{4}+8x^{3}
integral of sqrt(x)(x-3)	\int\:\sqrt{x}(x-3)dx
(\partial)/(\partial x)(x^2y^3(6-x-y))	\frac{\partial\:}{\partial\:x}(x^{2}\cdot\:y^{3}\cdot\:(6-x-y))
sum from n=3 to infinity of (3^n)/(n!)	\sum\:_{n=3}^{\infty\:}\frac{3^{n}}{n!}
integral of 9cos^2(x)	\int\:9\cos^{2}(x)dx
derivative of (x^2-3x)/(t^2+8)	derivative\:\frac{x^{2}-3x}{t^{2}+8}
integral of (y+1)/(2sqrt(y))	\int\:\frac{y+1}{2\sqrt{y}}dy
derivative of f(x)=sqrt((3x+1)),\at a=1	derivative\:f(x)=\sqrt{(3x+1)},\at\:a=1
derivative of f(x)=4sqrt(x)-8/(sqrt(x))	derivative\:f(x)=4\sqrt{x}-\frac{8}{\sqrt{x}}
limit as x approaches 1 of 7/(1-x)	\lim\:_{x\to\:1}(\frac{7}{1-x})
(\partial)/(\partial x)(y-e^{-2x^2y})	\frac{\partial\:}{\partial\:x}(y-e^{-2x^{2}y})
integral of (4+cos(x))/(x^2)	\int\:\frac{4+\cos(x)}{x^{2}}dx
integral of 2/(x^2+1)-x^2	\int\:\frac{2}{x^{2}+1}-x^{2}dx
derivative of f(2)=-x^2+6x-3	derivative\:f(2)=-x^{2}+6x-3
area x/(1+x^2),(x^2)/(1+x^3)	area\:\frac{x}{1+x^{2}},\frac{x^{2}}{1+x^{3}}
derivative of 1/4 sin(4x)	\frac{d}{dx}(\frac{1}{4}\sin(4x))
sum from n=1 to infinity of (2/3)^{n-1}	\sum\:_{n=1}^{\infty\:}(\frac{2}{3})^{n-1}
limit as x approaches o of f(x)	\lim\:_{x\to\:o}(f(x))
derivative of f(x)=x^3-2x^2-2x+1	derivative\:f(x)=x^{3}-2x^{2}-2x+1
integral of 1/((x^2+7)^{3/2)}	\int\:\frac{1}{(x^{2}+7)^{\frac{3}{2}}}dx
(dx)/(dt)=0	\frac{dx}{dt}=0
limit as h approaches 0 of 7/(3h)	\lim\:_{h\to\:0}(\frac{7}{3h})
integral of (x^3)/(1+9x^4)	\int\:\frac{x^{3}}{1+9x^{4}}dx
limit as x approaches 4 of (2x-8)/(x-4)	\lim\:_{x\to\:4}(\frac{2x-8}{x-4})
integral of x^2(x-5)sqrt(7-x)	\int\:x^{2}\cdot\:(x-5)\cdot\:\sqrt{7-x}dx
integral from 0 to 10 of \|x-5\|	\int\:_{0}^{10}\left\|x-5\right\|dx
tangent of 1/(2sqrt(x+2))	tangent\:\frac{1}{2\sqrt{x+2}}
integral of xe^{9x^2}	\int\:xe^{9x^{2}}dx
derivative of (48/x)	\frac{d}{dx}(\frac{48}{x})
derivative of e^{-x}+e^{2x}	\frac{d}{dx}(e^{-x}+e^{2x})
tangent of f(x)=5x-4x^2,(-3,-51)	tangent\:f(x)=5x-4x^{2},(-3,-51)
integral from 0 to 1 of x^n	\int\:_{0}^{1}x^{n}dx
derivative of 4/(e^x+e^{-x)}	derivative\:\frac{4}{e^{x}+e^{-x}}
y^{''}+2y^'+5y=0,y(0)=2,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=0,y(0)=2,y^{\prime\:}(0)=0
y^{''}-5y^'+6y=0	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=0
inverse oflaplace x/((x^2+1)(x^2+9))	inverselaplace\:\frac{x}{(x^{2}+1)(x^{2}+9)}
integral of t(t^2+1)^8	\int\:t(t^{2}+1)^{8}dt
integral from 1 to e^3 of (ln^3(x^2))/x	\int\:_{1}^{e^{3}}\frac{\ln^{3}(x^{2})}{x}dx
maclaurin x/(1-x^2)	maclaurin\:\frac{x}{1-x^{2}}
limit as x approaches 0 of ((10^x-1))/x	\lim\:_{x\to\:0}(\frac{(10^{x}-1)}{x})
limit as x approaches 1+of 4/((x-1)^3)	\lim\:_{x\to\:1+}(\frac{4}{(x-1)^{3}})
(\partial)/(\partial x)(-3cos(2x))	\frac{\partial\:}{\partial\:x}(-3\cos(2x))
integral of 5/(sqrt(1-9x^2))+7x	\int\:\frac{5}{\sqrt{1-9x^{2}}}+7xdx
(\partial)/(\partial x)(y^2-2xy)	\frac{\partial\:}{\partial\:x}(y^{2}-2xy)
derivative of x/(sqrt(2))	\frac{d}{dx}(\frac{x}{\sqrt{2}})
tangent of f(x)= 5/x ,\at x=4,x=5	tangent\:f(x)=\frac{5}{x},\at\:x=4,x=5
derivative of y=(9x^2-18x+18)e^{-4x}	derivative\:y=(9x^{2}-18x+18)e^{-4x}
integral of x^2e^{3x}	\int\:x^{2}e^{3x}dx
tangent of f(x)= 1/(5+x^2),\at x=2	tangent\:f(x)=\frac{1}{5+x^{2}},\at\:x=2
integral of cot^5(x)csc(x)	\int\:\cot^{5}(x)\csc(x)dx
derivative of \sqrt[4]{1+tan(t)}	derivative\:\sqrt[4]{1+\tan(t)}
integral of (x^2-x+28)/(x^3+7x)	\int\:\frac{x^{2}-x+28}{x^{3}+7x}dx
integral of (-2x^2+8x-20)/(x^2-4x+8)	\int\:\frac{-2x^{2}+8x-20}{x^{2}-4x+8}dx
sum from n=1 to infinity of 1/(1+3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{1+3^{n}}
xdy=4ydx	xdy=4ydx
integral of x^2sqrt((-2)^5+x^2)	\int\:x^{2}\sqrt{(-2)^{5}+x^{2}}dx
derivative of sin(xy)+pi	derivative\:\sin(xy)+π
(dy)/(dx)= x/(ysqrt(1+x))	\frac{dy}{dx}=\frac{x}{y\sqrt{1+x}}
integral of sqrt(3)cos(x)	\int\:\sqrt{3}\cos(x)dx
integral of (4x)/(x^2+1)	\int\:\frac{4x}{x^{2}+1}dx
integral of sqrt(e^{3t)}-1/(2sqrt(t))	\int\:\sqrt{e^{3t}}-\frac{1}{2\sqrt{t}}dt
slope of (3.6)(10.12)	slope\:(3.6)(10.12)
integral of tsec^2(2t)	\int\:t\sec^{2}(2t)dt
integral of (5(x^2+3))/(x(x^2+5))	\int\:\frac{5(x^{2}+3)}{x(x^{2}+5)}dx
laplacetransform (sin(t))^2	laplacetransform\:(\sin(t))^{2}
integral of 2t*(-cos(2t))	\int\:2t\cdot\:(-\cos(2t))dt
tangent of f(x)=e^x,\at x=5	tangent\:f(x)=e^{x},\at\:x=5
limit as x approaches 0 of 2/(1-2^{1/x)}	\lim\:_{x\to\:0}(\frac{2}{1-2^{\frac{1}{x}}})
t^3(dy)/(dt)+4t^2y=e^{-t},y(-1)=0	t^{3}\frac{dy}{dt}+4t^{2}y=e^{-t},y(-1)=0

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