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Popular Calculus Problems

derivative of uv	\frac{d}{dx}(uv)
integral of (x^2)/(1-x^3)	\int\:\frac{x^{2}}{1-x^{3}}dx
area y=8-x^2,y=x^2	area\:y=8-x^{2},y=x^{2}
derivative of (x^2+5)^3	derivative\:(x^{2}+5)^{3}
y^{''}+3y^'=12	y^{\prime\:\prime\:}+3y^{\prime\:}=12
integral of (e^{5x})/(e^{5x)+3}	\int\:\frac{e^{5x}}{e^{5x}+3}dx
x(dy)/(dx)-3y=0	x\frac{dy}{dx}-3y=0
limit as x approaches 4+of (x-4)/(4x-4)	\lim\:_{x\to\:4+}(\frac{x-4}{4x-4})
integral of (t^4)/(sqrt(1-t^{10))}	\int\:\frac{t^{4}}{\sqrt{1-t^{10}}}dt
integral of x^5*sin(x)	\int\:x^{5}\cdot\:\sin(x)dx
maclaurin ln(1-2y)	maclaurin\:\ln(1-2y)
integral of (3x-1)/(x^2-x-6)	\int\:\frac{3x-1}{x^{2}-x-6}dx
derivative of 2log_{10}(x)	\frac{d}{dx}(2\log_{10}(x))
integral from 1 to 2 of (4x^{3/2})	\int\:_{1}^{2}(4x^{\frac{3}{2}})dx
derivative of \sqrt[4]{x^3-x+3}	\frac{d}{dx}(\sqrt[4]{x^{3}-x+3})
(\partial)/(\partial y)(sin(2x+5y))	\frac{\partial\:}{\partial\:y}(\sin(2x+5y))
integral from 1 to 4 of 2sqrt(t)ln(t)	\int\:_{1}^{4}2\sqrt{t}\ln(t)dt
(\partial)/(\partial x)(8x^{6y})	\frac{\partial\:}{\partial\:x}(8x^{6y})
(\partial)/(\partial x)(20)	\frac{\partial\:}{\partial\:x}(20)
(\partial)/(\partial y)(1/4 x^2+y^2-1)	\frac{\partial\:}{\partial\:y}(\frac{1}{4}x^{2}+y^{2}-1)
derivative of g(x)=x^2+sin(x)	derivative\:g(x)=x^{2}+\sin(x)
parity f(x)=(x-3x^4)tan(x)	parity\:f(x)=(x-3x^{4})\tan(x)
integral of 200-20x-3x^2	\int\:200-20x-3x^{2}dx
derivative of ln(x*e^{2x})	\frac{d}{dx}(\ln(x)\cdot\:e^{2x})
(\partial)/(\partial x)(x^2y+3y^2-y)	\frac{\partial\:}{\partial\:x}(x^{2}y+3y^{2}-y)
((e^{4x^2})/(x^2))^'	(\frac{e^{4x^{2}}}{x^{2}})^{\prime\:}
integral of ((7x^9-20x^6))/(x^3)	\int\:\frac{(7x^{9}-20x^{6})}{x^{3}}dx
integral of (tan(x)+1/(tan(x)))^2	\int\:(\tan(x)+\frac{1}{\tan(x)})^{2}dx
x^2y^{''}-2y=sin(ln(x))	x^{2}y^{\prime\:\prime\:}-2y=\sin(\ln(x))
limit as x approaches-2 of 2x	\lim\:_{x\to\:-2}(2x)
integral of 1/(5x^7)	\int\:\frac{1}{5x^{7}}dx
maclaurin (arctan(x))/(x+1)	maclaurin\:\frac{\arctan(x)}{x+1}
derivative of 2/((1+x)^3)	derivative\:\frac{2}{(1+x)^{3}}
(\partial)/(\partial y)(y-cos(y))	\frac{\partial\:}{\partial\:y}(y-\cos(y))
integral from 0 to 1 of 8/(sqrt(x)(1+x))	\int\:_{0}^{1}\frac{8}{\sqrt{x}(1+x)}dx
derivative of f(x)=(x+2)^x	derivative\:f(x)=(x+2)^{x}
limit as x approaches 2 of x^2+3x-8	\lim\:_{x\to\:2}(x^{2}+3x-8)
integral of sqrt(9+8x-x^2)	\int\:\sqrt{9+8x-x^{2}}dx
integral of x^2e^{11x}	\int\:x^{2}e^{11x}dx
limit as x approaches 2 of 3x+5	\lim\:_{x\to\:2}(3x+5)
integral of cos^5(3x)sin^4(3x)	\int\:\cos^{5}(3x)\sin^{4}(3x)dx
integral from 1 to 2 of w^2ln(w)	\int\:_{1}^{2}w^{2}\ln(w)dw
derivative of 2sin(pix-y)	\frac{d}{dx}(2\sin(πx-y))
area 2/x ,-3x+7,-2x+4	area\:\frac{2}{x},-3x+7,-2x+4
derivative of ln(ln(10x))	\frac{d}{dx}(\ln(\ln(10x)))
y^'+(4/x)y=x^4	y^{\prime\:}+(\frac{4}{x})y=x^{4}
limit as x approaches-2 of tan((pix)/4)	\lim\:_{x\to\:-2}(\tan(\frac{πx}{4}))
derivative of (ln(x)/(ln(x)+2))	\frac{d}{dx}(\frac{\ln(x)}{\ln(x)+2})
derivative of 5x^4-2x^3-x^2	\frac{d}{dx}(5x^{4}-2x^{3}-x^{2})
integral of 16sin^2(x)	\int\:16\sin^{2}(x)dx
integral of sqrt(3x)	\int\:\sqrt{3x}dx
(\partial)/(\partial φ)(sin(θ)cos(φ))	\frac{\partial\:}{\partial\:φ}(\sin(θ)\cos(φ))
integral of sqrt(1+16x^2)	\int\:\sqrt{1+16x^{2}}dx
(x+1)y^'+y=x	(x+1)y^{\prime\:}+y=x
limit as x approaches-3 of 5	\lim\:_{x\to\:-3}(5)
derivative of (1+x^2(1+sqrt(x)))	\frac{d}{dx}((1+x^{2})(1+\sqrt{x}))
limit as x approaches-1 of (4x+3)/(2x+1)	\lim\:_{x\to\:-1}(\frac{4x+3}{2x+1})
integral of 10e^{x/(20)}	\int\:10e^{\frac{x}{20}}dx
integral of (1-2y)/y	\int\:\frac{1-2y}{y}dy
integral from 0 to 2 of xp(x-x^2)	\int\:_{0}^{2}xp(x-x^{2})dx
inverse oflaplace (s+1)/((s+1)^2+5)	inverselaplace\:\frac{s+1}{(s+1)^{2}+5}
derivative of y=x^5*x^4	derivative\:y=x^{5}\cdot\:x^{4}
derivative of 6sin(x-6xcos(x))	\frac{d}{dx}(6\sin(x)-6x\cos(x))
y^'+xy^{''}=0	y^{\prime\:}+xy^{\prime\:\prime\:}=0
integral of cos^2(nx)	\int\:\cos^{2}(nx)dx
integral from 0 to 1 of (x^2+7)e^{-x}	\int\:_{0}^{1}(x^{2}+7)e^{-x}dx
16y^{''}+16y^'-5y=0	16y^{\prime\:\prime\:}+16y^{\prime\:}-5y=0
derivative of f(x)=sqrt(2x)	derivative\:f(x)=\sqrt{2x}
integral of (x+8)/(x^2+25)	\int\:\frac{x+8}{x^{2}+25}dx
derivative of x^2e^{x^2}	\frac{d}{dx}(x^{2}e^{x^{2}})
derivative of x^2ln(4x)	\frac{d}{dx}(x^{2}\ln(4x))
integral of (4+x)/(sqrt(16-x^2))	\int\:\frac{4+x}{\sqrt{16-x^{2}}}dx
integral of 1/(2+x)	\int\:\frac{1}{2+x}dx
t^2y^{''}+ty^'+25y=0	t^{2}y^{\prime\:\prime\:}+ty^{\prime\:}+25y=0
(dy)/(dx)=3x	\frac{dy}{dx}=3x
limit as x approaches-1 of-x^2+1	\lim\:_{x\to\:-1}(-x^{2}+1)
y^{''}-12y^'+36y=0,y(0)=-2,y^'(0)=3	y^{\prime\:\prime\:}-12y^{\prime\:}+36y=0,y(0)=-2,y^{\prime\:}(0)=3
integral from 0 to 1 of 2/(t^2+1)	\int\:_{0}^{1}\frac{2}{t^{2}+1}dt
derivative of (e^x)/(4x^2+3)	derivative\:\frac{e^{x}}{4x^{2}+3}
derivative of f(x)=2pir^2+(1000)/r	derivative\:f(x)=2πr^{2}+\frac{1000}{r}
tangent of y= 6/(sqrt(x)),(36, 6/6)	tangent\:y=\frac{6}{\sqrt{x}},(36,\frac{6}{6})
(dy)/(dx)=-2y+e^x	\frac{dy}{dx}=-2y+e^{x}
integral from 0 to pi/6 of 4cos^5(3x)	\int\:_{0}^{\frac{π}{6}}4\cos^{5}(3x)dx
integral of 2/x+3sin(x)-4e^x	\int\:\frac{2}{x}+3\sin(x)-4e^{x}dx
(\partial)/(\partial x)(6ze^{xyz})	\frac{\partial\:}{\partial\:x}(6ze^{xyz})
y^'=20-4y	y^{\prime\:}=20-4y
laplacetransform e^{-43t}*e^{72t}cos(77t)	laplacetransform\:e^{-43t}\cdot\:e^{72t}\cos(77t)
integral of 5sin(x/4)	\int\:5\sin(\frac{x}{4})dx
d/(ds)(1/(s^2))	\frac{d}{ds}(\frac{1}{s^{2}})
derivative of 4x^{-1/8}	derivative\:4x^{-\frac{1}{8}}
derivative of ((3x^2)/((2x+4)))^3	derivative\:(\frac{3x^{2}}{(2x+4)})^{3}
(dy)/(dx)=((2y+5)^2)/((8x+9)^2)	\frac{dy}{dx}=\frac{(2y+5)^{2}}{(8x+9)^{2}}
tangent of y=x^2,(2,4)	tangent\:y=x^{2},(2,4)
f(x)=2\sqrt[4]{9-x^2}	f(x)=2\sqrt[4]{9-x^{2}}
limit as x approaches 3 of (x^2-3x)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{2}-3x}{x-3})
taylor x^5cos(x^3)	taylor\:x^{5}\cos(x^{3})
derivative of (2x^2+7^5)	\frac{d}{dx}((2x^{2}+7)^{5})
limit as x approaches 0 of (e^x+x)^{5/x}	\lim\:_{x\to\:0}((e^{x}+x)^{\frac{5}{x}})
integral of sin^2(2pix)	\int\:\sin^{2}(2πx)dx
limit as x approaches-2 of (x-2)/(\|x-2\|)	\lim\:_{x\to\:-2}(\frac{x-2}{\left\|x-2\right\|})

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