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Popular Calculus Problems

sum from n=1 to infinity of 1/n-1/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n}-\frac{1}{n+1}
integral of (e^{5x})/(e^{5x)+6}	\int\:\frac{e^{5x}}{e^{5x}+6}dx
tangent of-2xy-4x^4=-2+y	tangent\:-2xy-4x^{4}=-2+y
(\partial)/(\partial x)(12xy-x^3-y^3-7)	\frac{\partial\:}{\partial\:x}(12xy-x^{3}-y^{3}-7)
derivative of (18x+8x^2/((9+8x)^2))	\frac{d}{dx}(\frac{18x+8x^{2}}{(9+8x)^{2}})
integral of (cot(x))/(sin(x))	\int\:\frac{\cot(x)}{\sin(x)}dx
inverse oflaplace {(2/s-1/(s^3))^2}	inverselaplace\:\left\{(\frac{2}{s}-\frac{1}{s^{3}})^{2}\right\}
derivative of 8x^2(1-3x^5)	\frac{d}{dx}(8x^{2}(1-3x)^{5})
integral of x^2sec(x^3)	\int\:x^{2}\sec(x^{3})dx
integral of (sin(2x))e^{sin^2(x)}	\int\:(\sin(2x))e^{\sin^{2}(x)}dx
(sin(3x))^'	(\sin(3x))^{\prime\:}
limit as x approaches 1 of 4x-3	\lim\:_{x\to\:1}(4x-3)
integral of sin(4xy)	\int\:\sin(4xy)dx
taylor (1-x)^2	taylor\:(1-x)^{2}
derivative of x^4(2x-5^6)	\frac{d}{dx}(x^{4}(2x-5)^{6})
f(x)=(4x^2-1)/(x^3)	f(x)=\frac{4x^{2}-1}{x^{3}}
area x=sqrt(1/(12y)),y=x,x=16y	area\:x=\sqrt{\frac{1}{12y}},y=x,x=16y
(\partial)/(\partial x)(-(x/y))	\frac{\partial\:}{\partial\:x}(-(\frac{x}{y}))
derivative of x/(4-sqrt(16-x^2))	\frac{d}{dx}(\frac{x}{4-\sqrt{16-x^{2}}})
tangent of f(x)=5-2x^2,(-5,-45)	tangent\:f(x)=5-2x^{2},(-5,-45)
integral from 0 to 2 of (1+x)^{1/3}*2	\int\:_{0}^{2}(1+x)^{\frac{1}{3}}\cdot\:2dx
xy'+(1+x*cot(x))y=0	xy\prime\:+(1+x\cdot\:\cot(x))y=0
derivative of (x-1^2(x+2))	\frac{d}{dx}((x-1)^{2}(x+2))
area y=3-x^2,y=11-6x	area\:y=3-x^{2},y=11-6x
integral from 0 to 4 of x/(sqrt(1+2x))	\int\:_{0}^{4}\frac{x}{\sqrt{1+2x}}dx
derivative of-(2x)/((x^2-1)^2)	derivative\:-\frac{2x}{(x^{2}-1)^{2}}
derivative of ln(4/x)	\frac{d}{dx}(\ln(\frac{4}{x}))
derivative of 5/(2x^3)	derivative\:\frac{5}{2x^{3}}
limit as w approaches 0 of (sec(2w)-1)/(wsec(2w))	\lim\:_{w\to\:0}(\frac{\sec(2w)-1}{w\sec(2w)})
area y=sqrt(x),y=sqrt(8-x),y=0	area\:y=\sqrt{x},y=\sqrt{8-x},y=0
y^'=y^2sin(x^2),y(-2)= 1/3	y^{\prime\:}=y^{2}\sin(x^{2}),y(-2)=\frac{1}{3}
limit as x approaches 0 of g(x)(f(x))	\lim\:_{x\to\:0}(g(x)(f(x)))
integral from 0 to 1 of (e^x)/x	\int\:_{0}^{1}\frac{e^{x}}{x}dx
derivative of (x^2+40x/5)	\frac{d}{dx}(\frac{x^{2}+40x}{5})
area f(x)=2+x-x^2,0,3	area\:f(x)=2+x-x^{2},0,3
limit as h approaches 0 of 8x+4h+9	\lim\:_{h\to\:0}(8x+4h+9)
derivative of x^3-3x-sqrt(x)	\frac{d}{dx}(x^{3}-3x-\sqrt{x})
derivative of arccos(2x)	derivative\:\arccos(2x)
tangent of f(x)=sqrt(x+6),\at x=1	tangent\:f(x)=\sqrt{x+6},\at\:x=1
derivative of (x^2)/(7+6x)	derivative\:\frac{x^{2}}{7+6x}
derivative of sqrt({R)(x(x)^2-x^2})	\frac{d}{dx}(\sqrt{{R}(x)(x)^{2}-x^{2}})
integral of (sec^2(1/x))/(x^2)	\int\:\frac{\sec^{2}(\frac{1}{x})}{x^{2}}dx
integral of (cot^5(β))/(sqrt(sin(β)))	\int\:\frac{\cot^{5}(β)}{\sqrt{\sin(β)}}dβ
5(dy)/(dt)+y=5t	5\frac{dy}{dt}+y=5t
integral of 30x^3sqrt(1+x^2)	\int\:30x^{3}\sqrt{1+x^{2}}dx
integral of (-4x^2)/(sqrt(4x-x^2))	\int\:\frac{-4x^{2}}{\sqrt{4x-x^{2}}}dx
limit as x approaches 0 of x/(1+x^2)	\lim\:_{x\to\:0}(\frac{x}{1+x^{2}})
y^'=cos(t)y(1-y/(100))	y^{\prime\:}=\cos(t)y(1-\frac{y}{100})
sum from n=1 to infinity of 1/(4^n-3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{4^{n}-3^{n}}
2(2xy+4y-3)dx+(x+2)^2dy=0	2(2xy+4y-3)dx+(x+2)^{2}dy=0
integral of sin(5x)cos(3x)	\int\:\sin(5x)\cos(3x)dx
sum from n=1 to infinity of (3n)/(n^2+2)	\sum\:_{n=1}^{\infty\:}\frac{3n}{n^{2}+2}
integral from 0 to 2pi of 1	\int\:_{0}^{2π}1
integral from-infinity to 0 of 9^x	\int\:_{-\infty\:}^{0}9^{x}dx
integral of 5m(12m^3-10m)	\int\:5m(12m^{3}-10m)dm
slope of 2x^2+10x-4/(x^2),\at x=-5	slope\:2x^{2}+10x-\frac{4}{x^{2}},\at\:x=-5
x((dy)/(dx))=y+sqrt(x^2-y^2)	x(\frac{dy}{dx})=y+\sqrt{x^{2}-y^{2}}
integral from 0 to 1 of xarcsin(x)	\int\:_{0}^{1}x\arcsin(x)dx
(\partial)/(\partial x)(3xz)	\frac{\partial\:}{\partial\:x}(3xz)
integral of (8e^x)/(e^{2x)-16}	\int\:\frac{8e^{x}}{e^{2x}-16}dx
integral from 0 to pi/2 of sin(2θ)	\int\:_{0}^{\frac{π}{2}}\sin(2θ)dθ
derivative of 3ln(sec(x+tan(x)))	\frac{d}{dx}(3\ln(\sec(x)+\tan(x)))
y^'-e^{x+1}=0	y^{\prime\:}-e^{x+1}=0
integral of sec(x/4)	\int\:\sec(\frac{x}{4})dx
y^{''}+9y=2sin(x)+cos(x)	y^{\prime\:\prime\:}+9y=2\sin(x)+\cos(x)
(dy)/(dx)-xy=x	\frac{dy}{dx}-xy=x
25y^{''}+90y^'+81y=0	25y^{\prime\:\prime\:}+90y^{\prime\:}+81y=0
derivative of 656112^{sqrt(x)}	\frac{d}{dx}(656112^{\sqrt{x}})
integral of 1/(sin(2x))	\int\:\frac{1}{\sin(2x)}dx
derivative of 3sec(8x)	\frac{d}{dx}(3\sec(8x))
derivative of 9excos(x)	derivative\:9ex\cos(x)
integral of (x^4)/(5x^5+4)	\int\:\frac{x^{4}}{5x^{5}+4}dx
derivative of 2e^{2e^x+x}	\frac{d}{dx}(2e^{2e^{x}+x})
integral of 1/(x^2sqrt(x^2-11))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-11}}dx
derivative of e^{(ln(x)/x})	\frac{d}{dx}(e^{\frac{\ln(x)}{x}})
(dy)/(dx)=e^{9x-8y}	\frac{dy}{dx}=e^{9x-8y}
dy+0.15(y-30)dx=0	dy+0.15(y-30)dx=0
derivative of 1/3 x^3-2x^2+3x-4	derivative\:\frac{1}{3}x^{3}-2x^{2}+3x-4
limit as x approaches infinity of 1+8/x	\lim\:_{x\to\:\infty\:}(1+\frac{8}{x})
derivative of 8x^2e^x	derivative\:8x^{2}e^{x}
derivative of sqrt(1-121x^2)arccos(11x)	\frac{d}{dx}(\sqrt{1-121x^{2}}\arccos(11x))
inverse oflaplace s/(s^2+64)	inverselaplace\:\frac{s}{s^{2}+64}
integral of (x^3-4x-6)	\int\:(x^{3}-4x-6)dx
derivative of (3x^2+2(2x-3))	\frac{d}{dx}((3x^{2}+2)(2x-3))
integral of (7x^2)/((9+x^2)^2)	\int\:\frac{7x^{2}}{(9+x^{2})^{2}}dx
integral from 0 to 1 of 16sin^4(x)	\int\:_{0}^{1}16\sin^{4}(x)dx
limit as x approaches 3 of (x-3)/((x-3))	\lim\:_{x\to\:3}(\frac{x-3}{(x-3)})
y^{''}-2y^'+10y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=0
derivative of e^{4/x}	\frac{d}{dx}(e^{\frac{4}{x}})
limit as x approaches 2 of 5x-6	\lim\:_{x\to\:2}(5x-6)
derivative of (4x-8/(x-5))	\frac{d}{dx}(\frac{4x-8}{x-5})
integral of cot(4t)sqrt(1-sin^2(4t))	\int\:\cot(4t)\sqrt{1-\sin^{2}(4t)}dt
integral of (5x^2-5x+14)/((x-2)(x^2+4))	\int\:\frac{5x^{2}-5x+14}{(x-2)(x^{2}+4)}dx
limit as x approaches-3 of x/(x^2-9)	\lim\:_{x\to\:-3}(\frac{x}{x^{2}-9})
integral of 1/2 xe^{2x}	\int\:\frac{1}{2}xe^{2x}dx
integral of 3cos(x)y+5x^4z^2	\int\:3\cos(x)y+5x^{4}z^{2}dx
integral of e^{x+sin(y)}cos(y)	\int\:e^{x+\sin(y)}\cos(y)dy
sum from n=1 to infinity of 1/(n*(n+1))	\sum\:_{n=1}^{\infty\:}\frac{1}{n\cdot\:(n+1)}
integral of (1+sqrt(x))/(-xsqrt(x))	\int\:\frac{1+\sqrt{x}}{-x\sqrt{x}}dx
integral from 0 to 1 of-(x^2-x)	\int\:_{0}^{1}-(x^{2}-x)dx

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