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Popular Calculus Problems

limit as x approaches 2 of (x+2)/x	\lim\:_{x\to\:2}(\frac{x+2}{x})
(\partial)/(\partial y)(xydx)	\frac{\partial\:}{\partial\:y}(xydx)
integral of 3+x	\int\:3+xdx
derivative of (9x^6+8x^3^4)	\frac{d}{dx}((9x^{6}+8x^{3})^{4})
limit as x approaches+1+of x	\lim\:_{x\to\:+1+}(x)
limit as x approaches 9 of 5/(x+5)	\lim\:_{x\to\:9}(\frac{5}{x+5})
sum from n=0 to infinity of (x-3)^n	\sum\:_{n=0}^{\infty\:}(x-3)^{n}
derivative of arctan(sqrt(3t))	derivative\:\arctan(\sqrt{3t})
y^{''}+2y^'+17y=0,y(0)=3,y^'(0)=-2	y^{\prime\:\prime\:}+2y^{\prime\:}+17y=0,y(0)=3,y^{\prime\:}(0)=-2
integral of e^{-4x}sin(bx)	\int\:e^{-4x}\sin(bx)dx
integral from 5 to 3 of 2	\int\:_{5}^{3}2dx
inverse oflaplace (s+2)/(s(s+1))	inverselaplace\:\frac{s+2}{s(s+1)}
integral of 2cot^3(x)csc^3(x)	\int\:2\cot^{3}(x)\csc^{3}(x)dx
limit as x approaches infinity of-2x^4	\lim\:_{x\to\:\infty\:}(-2x^{4})
integral of 1/(1+r^2)	\int\:\frac{1}{1+r^{2}}dr
(\partial)/(\partial x)(xe^{x^3y})	\frac{\partial\:}{\partial\:x}(xe^{x^{3}y})
derivative of pix^2h	\frac{d}{dx}(πx^{2}h)
integral of (12)/(x(x^2+25))	\int\:\frac{12}{x(x^{2}+25)}dx
derivative of csc^2(x)-4	derivative\:\csc^{2}(x)-4
(x+6xy^4)dx+e^{x^2}y^3dy=0	(x+6xy^{4})dx+e^{x^{2}}y^{3}dy=0
integral of 2/(3\sqrt[3]{x^2)}	\int\:\frac{2}{3\sqrt[3]{x^{2}}}dx
y^{''}+16y=sec(4x)	y^{\prime\:\prime\:}+16y=\sec(4x)
derivative of \|x^3\|	\frac{d}{dx}(\left\|x^{3}\right\|)
integral from-1 to 1 of 2-\|x\|-x^4	\int\:_{-1}^{1}2-\left\|x\right\|-x^{4}dx
(dy)/(dx)=y^4sin(x)	\frac{dy}{dx}=y^{4}\sin(x)
integral of (2(2t-1))/(t(3t^2+4t-1))	\int\:\frac{2(2t-1)}{t(3t^{2}+4t-1)}dt
integral of (3x)/(sqrt(x^2+x+1))	\int\:\frac{3x}{\sqrt{x^{2}+x+1}}dx
xe^{(x+2)}	xe^{(x+2)}
area 2x^2ln(x),8ln(x)	area\:2x^{2}\ln(x),8\ln(x)
integral of ((x^3))/3	\int\:\frac{(x^{3})}{3}dx
derivative of y=3x^2+17x+10	derivative\:y=3x^{2}+17x+10
(\partial)/(\partial x)(x^2y+x+y)	\frac{\partial\:}{\partial\:x}(x^{2}y+x+y)
2y^{''}-2y^'+5y=0	2y^{\prime\:\prime\:}-2y^{\prime\:}+5y=0
derivative of (e^x/(3+e^x))	\frac{d}{dx}(\frac{e^{x}}{3+e^{x}})
derivative of 7sin(x-2x^3)	\frac{d}{dx}(7\sin(x)-2x^{3})
integral of (x^2+36x+36)/(x^3-4x)	\int\:\frac{x^{2}+36x+36}{x^{3}-4x}dx
limit as x approaches 1 of (x-1)/(ln(x))	\lim\:_{x\to\:1}(\frac{x-1}{\ln(x)})
derivative of (2x^2+3(5x+3))	\frac{d}{dx}((2x^{2}+3)(5x+3))
121y^{''}-64y=0	121y^{\prime\:\prime\:}-64y=0
integral from 1 to sqrt(3 of) 6/(1+x^2)	\int\:_{1}^{\sqrt{3}}\frac{6}{1+x^{2}}dx
integral of 6e^{-0.1x}	\int\:6e^{-0.1x}dx
taylor sin(x), pi/2	taylor\:\sin(x),\frac{π}{2}
integral of (x^5+x^4)^7(5x^4+4x^3)	\int\:(x^{5}+x^{4})^{7}(5x^{4}+4x^{3})dx
integral of (-4/(sqrt(3-3x^2)))	\int\:(-\frac{4}{\sqrt{3-3x^{2}}})dx
limit as x approaches infinity of x(e^{1/x}-1)	\lim\:_{x\to\:\infty\:}(x(e^{\frac{1}{x}}-1))
integral of (1-e^x)/(e^x+1)	\int\:\frac{1-e^{x}}{e^{x}+1}dx
derivative of g(x)=((9+6x)/(7-4x))	derivative\:g(x)=(\frac{9+6x}{7-4x})
(\partial)/(\partial z)(y/z)	\frac{\partial\:}{\partial\:z}(\frac{y}{z})
derivative of (sqrt(x))/(1+x)	derivative\:\frac{\sqrt{x}}{1+x}
derivative of (Ax^2+Bxe^{-x})	\frac{d}{dx}((Ax^{2}+Bx)e^{-x})
d/(dt)((2t)/(t^2+2))	\frac{d}{dt}(\frac{2t}{t^{2}+2})
derivative of arccot(3x)	derivative\:\arccot(3x)
sum from n=1 to infinity of (n!)/(14^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{14^{n}}
(\partial)/(\partial y)(-2sec^2(3x-2y+1))	\frac{\partial\:}{\partial\:y}(-2\sec^{2}(3x-2y+1))
derivative of tan(5x+1)	\frac{d}{dx}(\tan(5x+1))
xy^2y^'=x+6	xy^{2}y^{\prime\:}=x+6
sum from n=1 to infinity of 7/(n^6)	\sum\:_{n=1}^{\infty\:}\frac{7}{n^{6}}
derivative of y=(sqrt(x)-1)/(sqrt(x)+1)	derivative\:y=\frac{\sqrt{x}-1}{\sqrt{x}+1}
limit as x approaches-3 of g(x)	\lim\:_{x\to\:-3}(g(x))
derivative of-(40x)/(9-5x^2)	derivative\:-\frac{40x}{9-5x^{2}}
derivative of sin(xln(8x))	\frac{d}{dx}(\sin(x)\ln(8x))
d/(d{x)}({x}^2+{y}{z})	\frac{d}{d{x}}({x}^{2}+{y}{z})
tangent of y=8x^2-x^3(2.24)	tangent\:y=8x^{2}-x^{3}(2.24)
sum from n=0 to infinity of ((8^n))/(n!)	\sum\:_{n=0}^{\infty\:}\frac{(8^{n})}{n!}
y^'+y=y^2	y^{\prime\:}+y=y^{2}
derivative of 30x^4y^7-24x^{12}y^3	\frac{d}{dx}(30x^{4}y^{7}-24x^{12}y^{3})
integral of 9xe^{15x}	\int\:9xe^{15x}dx
derivative of-e^{x^2}	\frac{d}{dx}(-e^{x^{2}})
tangent of f(x)=sqrt(7x),(7,7)	tangent\:f(x)=\sqrt{7x},(7,7)
6e^{2x-y}dx=dy	6e^{2x-y}dx=dy
integral of 1/(x(x-a))	\int\:\frac{1}{x(x-a)}dx
(\partial)/(\partial y)(x+ln(y))	\frac{\partial\:}{\partial\:y}(x+\ln(y))
integral from 1 to e^5 of x^4ln(x)	\int\:_{1}^{e^{5}}x^{4}\ln(x)dx
derivative of y=(x^2-1)/(x^2+1)	derivative\:y=\frac{x^{2}-1}{x^{2}+1}
derivative of h(t)=65-55cos((pit)/(15))	derivative\:h(t)=65-55\cos(\frac{πt}{15})
integral from-1 to 2 of (3x+1)	\int\:_{-1}^{2}(3x+1)dx
integral of 1/(x^3sqrt(x^2-49))	\int\:\frac{1}{x^{3}\sqrt{x^{2}-49}}dx
inverse oflaplace (x^2+1)/(x^2-x-6)	inverselaplace\:\frac{x^{2}+1}{x^{2}-x-6}
integral of ln(1+sqrt(x))	\int\:\ln(1+\sqrt{x})dx
integral of (\sqrt[m]{x}-1)/(\sqrt[m]{x)}	\int\:\frac{\sqrt[m]{x}-1}{\sqrt[m]{x}}dx
area 5cos(9x),5-5cos(9x)	area\:5\cos(9x),5-5\cos(9x)
derivative of f(x)=8sin^6(sqrt(x))	derivative\:f(x)=8\sin^{6}(\sqrt{x})
limit as x approaches 4+of 1/(\|4-x\|)	\lim\:_{x\to\:4+}(\frac{1}{\left\|4-x\right\|})
integral of sqrt(t)-4cos(t)	\int\:\sqrt{t}-4\cos(t)dt
slope of y=x^3,\at x=5	slope\:y=x^{3},\at\:x=5
(2r-1)/t dr+(r-2r^2)/(t^2-1)dt=0	\frac{2r-1}{t}dr+\frac{r-2r^{2}}{t^{2}-1}dt=0
derivative of 3x^4-2x^3-12x^2+18x+15	\frac{d}{dx}(3x^{4}-2x^{3}-12x^{2}+18x+15)
derivative of g(x)=x+sqrt(x)	derivative\:g(x)=x+\sqrt{x}
area 2sin(x),3cos(x)	area\:2\sin(x),3\cos(x)
derivative of 1/(ln(x^2))	\frac{d}{dx}(\frac{1}{\ln(x^{2})})
(\partial)/(\partial y)(sqrt(x^2-y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{x^{2}-y^{2}})
(\partial)/(\partial θ)(ρsin(φ)cos(θ))	\frac{\partial\:}{\partial\:θ}(ρ\sin(φ)\cos(θ))
(\partial)/(\partial y)(ln(x^2y^2))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}y^{2}))
(\partial)/(\partial x)(arctan(5x))	\frac{\partial\:}{\partial\:x}(\arctan(5x))
(9y^2-xy)dx+x^2dy=0	(9y^{2}-xy)dx+x^{2}dy=0
integral of 1/(x^2+10x+29)	\int\:\frac{1}{x^{2}+10x+29}dx
derivative of f(x)=(arcsec(x))^{13}	derivative\:f(x)=(\arcsec(x))^{13}
integral of 3xsin^2(x)	\int\:3x\sin^{2}(x)dx
integral from 0 to 1 of-1/(x-5)+2/(x-2)	\int\:_{0}^{1}-\frac{1}{x-5}+\frac{2}{x-2}dx
derivative of ln(x^{-2})	\frac{d}{dx}(\ln(x^{-2}))

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