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Popular Calculus Problems

derivative of arctan(sqrt((x-y/x)))	\frac{d}{dx}(\arctan(\sqrt{\frac{x-y}{x}}))
derivative of 576pi-4pi^3x^2+4pix^2	derivative\:576π-4π^{3}x^{2}+4πx^{2}
limit as x approaches 1 of 4x^3-e^{x-1}	\lim\:_{x\to\:1}(4x^{3}-e^{x-1})
integral of ((ln(x))^{14})/x	\int\:\frac{(\ln(x))^{14}}{x}dx
integral of sin^5(tco)s^6t	\int\:\sin^{5}(tco)s^{6}tdt
x^'=-x/(x+1)	x^{\prime\:}=-\frac{x}{x+1}
tangent of y=9-2x^2,(2,1)	tangent\:y=9-2x^{2},(2,1)
integral from 0 to (3pi)/2 of cos^3(21x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(21x)dx
taylor x/(10-9x)	taylor\:\frac{x}{10-9x}
integral of (25-x^2)^{-3/2}	\int\:(25-x^{2})^{-\frac{3}{2}}dx
derivative of 10^{2x}	\frac{d}{dx}(10^{2x})
(db)/(db)	\frac{db}{db}
derivative of (3x^4+3x)^2	derivative\:(3x^{4}+3x)^{2}
sum from n=0 to infinity of 3/(7^n)	\sum\:_{n=0}^{\infty\:}\frac{3}{7^{n}}
derivative of (7x+1(x^4-x^3-9x))	\frac{d}{dx}((7x+1)(x^{4}-x^{3}-9x))
y^{''}+4y^'+3y=2x	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=2x
derivative of (e^x/(2x^2))	\frac{d}{dx}(\frac{e^{x}}{2x^{2}})
integral of sqrt(1-sin^2(x))	\int\:\sqrt{1-\sin^{2}(x)}dx
derivative of sqrt(16+x)	\frac{d}{dx}(\sqrt{16+x})
limit as x approaches 0 of 2^{-x}	\lim\:_{x\to\:0}(2^{-x})
integral from 1 to 2 of sqrt(x-1)-x+1	\int\:_{1}^{2}\sqrt{x-1}-x+1dx
tangent of f(x)=x^{sin(x)},(pi/2 , pi/2)	tangent\:f(x)=x^{\sin(x)},(\frac{π}{2},\frac{π}{2})
integral of x^2(x^3-1)^3	\int\:x^{2}(x^{3}-1)^{3}dx
area y=x,y=(x-2)^2	area\:y=x,y=(x-2)^{2}
limit as x approaches 0 of (2x)/(x+4)	\lim\:_{x\to\:0}(\frac{2x}{x+4})
derivative of (1-tan(x)/(1+tan(x)))	\frac{d}{dx}(\frac{1-\tan(x)}{1+\tan(x)})
tangent of (10x)/(x^2-6)	tangent\:\frac{10x}{x^{2}-6}
f(x)=x^2ln(x)	f(x)=x^{2}\ln(x)
integral from 0 to 3 of x^3-6x	\int\:_{0}^{3}x^{3}-6xdx
integral of e^{-x/(50)}	\int\:e^{-\frac{x}{50}}dx
y^{''}+20y^'+200y=150	y^{\prime\:\prime\:}+20y^{\prime\:}+200y=150
derivative of 5/(\sqrt[4]{x)}	derivative\:\frac{5}{\sqrt[4]{x}}
(\partial)/(\partial x)(arcsin(4x))	\frac{\partial\:}{\partial\:x}(\arcsin(4x))
(\partial)/(\partial y)(x^2sin(y))	\frac{\partial\:}{\partial\:y}(x^{2}\sin(y))
integral from 1 to 7 of 4/(x^2)	\int\:_{1}^{7}\frac{4}{x^{2}}dx
integral from-64 to 1 of 1/(x^{1/3)}	\int\:_{-64}^{1}\frac{1}{x^{\frac{1}{3}}}dx
integral of sin(4x-2)sin(3x+5)	\int\:\sin(4x-2)\sin(3x+5)dx
area 4cos(3x),4-4cos(3x),[0, pi/3 ]	area\:4\cos(3x),4-4\cos(3x),[0,\frac{π}{3}]
tangent of-2x^3-4x^2,\at x=1	tangent\:-2x^{3}-4x^{2},\at\:x=1
integral of cot^2(x)csc^4(x)	\int\:\cot^{2}(x)\csc^{4}(x)dx
(\partial)/(\partial x)(sin(3x+2y))	\frac{\partial\:}{\partial\:x}(\sin(3x+2y))
inverse oflaplace s/((s^2+16)^2)	inverselaplace\:\frac{s}{(s^{2}+16)^{2}}
4y^{''}+6y^'+7y=0	4y^{\prime\:\prime\:}+6y^{\prime\:}+7y=0
derivative of sin(e^{2xy}+e^{sin(2xy)})	\frac{d}{dx}(\sin(e^{2xy})+e^{\sin(2xy)})
tangent of y=sqrt(4x+33),(4,7)	tangent\:y=\sqrt{4x+33},(4,7)
integral of (2x)^{1/2}	\int\:(2x)^{\frac{1}{2}}dx
integral of x^2sqrt(1+(2x)^2)	\int\:x^{2}\sqrt{1+(2x)^{2}}dx
integral of 1/(cot(3x))	\int\:\frac{1}{\cot(3x)}dx
y^'=(x^2+3)/y ,y(0)=1	y^{\prime\:}=\frac{x^{2}+3}{y},y(0)=1
maclaurin xe^x	maclaurin\:xe^{x}
limit as x approaches-4 of sqrt(16-x^2)	\lim\:_{x\to\:-4}(\sqrt{16-x^{2}})
integral of x/((x-1)(x^2+2x+2)^2)	\int\:\frac{x}{(x-1)(x^{2}+2x+2)^{2}}dx
limit as x approaches 0+of 2/x	\lim\:_{x\to\:0+}(\frac{2}{x})
x(dy)/(dx)+8y=e^{x^8}	x\frac{dy}{dx}+8y=e^{x^{8}}
limit as x approaches 0+of \|1+1/(x-1)\|	\lim\:_{x\to\:0+}(\left\|1+\frac{1}{x-1}\right\|)
derivative of 2x^2+8x+10	\frac{d}{dx}(2x^{2}+8x+10)
limit as x approaches-3 of sqrt(7+x)	\lim\:_{x\to\:-3}(\sqrt{7+x})
limit as x approaches-3 of x+3	\lim\:_{x\to\:-3}(x+3)
derivative of ((x+1)(x+2))/((x-1)(x-2))	derivative\:\frac{(x+1)(x+2)}{(x-1)(x-2)}
integral of [tan(5x)+csc^3(3θ)]	\int\:[\tan(5x)+\csc^{3}(3θ)]dθ
tangent of f(x)=(e^x)/x ,(1,e)	tangent\:f(x)=\frac{e^{x}}{x},(1,e)
integral of sqrt(25x^2+4)	\int\:\sqrt{25x^{2}+4}dx
integral from-ln(4) to 0 of sqrt(3)e^x	\int\:_{-\ln(4)}^{0}\sqrt{3}e^{x}dx
derivative of 2cos(x)+cos^2(x)	derivative\:2\cos(x)+\cos^{2}(x)
integral of sqrt(9x^2+1)	\int\:\sqrt{9x^{2}+1}dx
integral of 1/(x^2-4x-12)	\int\:\frac{1}{x^{2}-4x-12}dx
inverse oflaplace (20)/(s(s^2+4))	inverselaplace\:\frac{20}{s(s^{2}+4)}
integral of 1/(1+cos(3x))	\int\:\frac{1}{1+\cos(3x)}dx
(\partial)/(\partial x)(22xye^{-x^2-y^2})	\frac{\partial\:}{\partial\:x}(22xye^{-x^{2}-y^{2}})
derivative of-0.1x^2+1.2x+98.4	derivative\:-0.1x^{2}+1.2x+98.4
2xydx+(x^2+2y)dy=0	2xydx+(x^{2}+2y)dy=0
derivative of y=tan^2(x)	derivative\:y=\tan^{2}(x)
integral of 1/(sin(t))	\int\:\frac{1}{\sin(t)}dt
integral of (2x-3x^2)^{-0.5}	\int\:(2x-3x^{2})^{-0.5}dx
integral from 0 to infinity of y^2e^{-y}	\int\:_{0}^{\infty\:}y^{2}e^{-y}dy
integral of (x^4)/(x^3+x^2-x-1)	\int\:\frac{x^{4}}{x^{3}+x^{2}-x-1}dx
integral of s/(sqrt(2s+3))	\int\:\frac{s}{\sqrt{2s+3}}ds
tangent of f(x)=6+5x^2-2x^3,\at x=2	tangent\:f(x)=6+5x^{2}-2x^{3},\at\:x=2
integral of sqrt(x)(3+5x)	\int\:\sqrt{x}(3+5x)dx
limit as x approaches 2 of 3f(x)+2g(x)(x)^2	\lim\:_{x\to\:2}(3f(x)+2g(x)(x)^{2})
inverse oflaplace (2s^2+5s+5)/((s+1)^3)	inverselaplace\:\frac{2s^{2}+5s+5}{(s+1)^{3}}
tangent of (5/x),\at x=4	tangent\:(\frac{5}{x}),\at\:x=4
integral of 3e^x+5sin(x)	\int\:3e^{x}+5\sin(x)dx
tangent of y=(x^3-25x)^8,(5,0)	tangent\:y=(x^{3}-25x)^{8},(5,0)
limit as x approaches 4 of sqrt(x^3+4x)	\lim\:_{x\to\:4}(\sqrt{x^{3}+4x})
implicit (dy)/(dx),x=cos(2y)	implicit\:\frac{dy}{dx},x=\cos(2y)
limit as x approaches 0 of 5/2 x^2	\lim\:_{x\to\:0}(\frac{5}{2}x^{2})
integral of sin(x)sin((2x)/3)	\int\:\sin(x)\sin(\frac{2x}{3})dx
derivative of e^{a(e^x-1})	\frac{d}{dx}(e^{a(e^{x}-1)})
derivative of 1/s	derivative\:\frac{1}{s}
area y=27-x^2,y=6x,y= 2/5 x	area\:y=27-x^{2},y=6x,y=\frac{2}{5}x
tangent of sqrt(sin(3x))	tangent\:\sqrt{\sin(3x)}
(dy)/(dx)=3x(x-1)	\frac{dy}{dx}=3x(x-1)
limit as x approaches 0 of 3x^3+6x^2+7x	\lim\:_{x\to\:0}(3x^{3}+6x^{2}+7x)
integral of x(2x+1)^{1/2}	\int\:x(2x+1)^{\frac{1}{2}}dx
(\partial)/(\partial x)(x/1)	\frac{\partial\:}{\partial\:x}(\frac{x}{1})
inverse oflaplace ((s+1))/(s(s^2+4s+4))	inverselaplace\:\frac{(s+1)}{s(s^{2}+4s+4)}
derivative of (x^2/(x+y))	\frac{d}{dx}(\frac{x^{2}}{x+y})
(\partial)/(\partial x)(x+ycos(x))	\frac{\partial\:}{\partial\:x}(x+y\cos(x))
integral of (sin^2(x))/2	\int\:\frac{\sin^{2}(x)}{2}dx

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