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Popular Calculus Problems

(dy)/(dx)=2xy^2+3x^2y^2,y(1)=-1	\frac{dy}{dx}=2xy^{2}+3x^{2}y^{2},y(1)=-1
integral of (4x+3)/(sqrt(1-x^2))	\int\:\frac{4x+3}{\sqrt{1-x^{2}}}dx
derivative of sin(4x+7x^4+e^{1-x^2})	\frac{d}{dx}(\sin(4x+7x^{4})+e^{1-x^{2}})
integral of (x^2+24x-9)/(x^3-9x)	\int\:\frac{x^{2}+24x-9}{x^{3}-9x}dx
limit as x approaches pi/2 of-cos(x)	\lim\:_{x\to\:\frac{π}{2}}(-\cos(x))
derivative of y=(6x^2+6x+2)/(sqrt(x))	derivative\:y=\frac{6x^{2}+6x+2}{\sqrt{x}}
derivative of 5cos(x)	derivative\:5\cos(x)
(\partial)/(\partial x)(xln(t))	\frac{\partial\:}{\partial\:x}(x\ln(t))
derivative of e^x-e^{-x}	derivative\:e^{x}-e^{-x}
integral of sin(x)*x	\int\:\sin(x)\cdot\:xdx
derivative of sqrt(cos(e^{x^5sin(x))})	\frac{d}{dx}(\sqrt{\cos(e^{x^{5}\sin(x)})})
derivative of-6/(x^3)	derivative\:-\frac{6}{x^{3}}
integral of sqrt(x)arctan(sqrt(x))	\int\:\sqrt{x}\arctan(\sqrt{x})dx
(\partial)/(\partial x)(x^4+12xy^2+2y^4)	\frac{\partial\:}{\partial\:x}(x^{4}+12xy^{2}+2y^{4})
derivative of y=(2x-9)/(3x+7)	derivative\:y=\frac{2x-9}{3x+7}
integral of (7^x)/(sqrt(1-7^{2x))}	\int\:\frac{7^{x}}{\sqrt{1-7^{2x}}}dx
derivative of e^{-3}	\frac{d}{dx}(e^{-3})
derivative of (1-x^{1/2})	\frac{d}{dx}((1-x)^{\frac{1}{2}})
(\partial)/(\partial x)(cos(x)sin(y))	\frac{\partial\:}{\partial\:x}(\cos(x)\sin(y))
y^{''}-10y^'+61y=0	y^{\prime\:\prime\:}-10y^{\prime\:}+61y=0
inverse oflaplace (56s)/(s^2+196)	inverselaplace\:\frac{56s}{s^{2}+196}
(dy)/(dx)=-2xtan(y),y(0)= pi/2	\frac{dy}{dx}=-2x\tan(y),y(0)=\frac{π}{2}
(dx)/(dt)=x(1-0.0004x)	\frac{dx}{dt}=x(1-0.0004x)
integral from 1 to 2 of 9(ln(x))/(x^2)	\int\:_{1}^{2}9\frac{\ln(x)}{x^{2}}dx
integral of 1/(sqrt(x(x+1)))	\int\:\frac{1}{\sqrt{x(x+1)}}dx
tangent of f(x)=sqrt(x-1),(10,3)	tangent\:f(x)=\sqrt{x-1},(10,3)
integral from 0 to 3 of sqrt(4x+5)	\int\:_{0}^{3}\sqrt{4x+5}dx
area x=-3,x=-1,y=x^3+8,y=0	area\:x=-3,x=-1,y=x^{3}+8,y=0
(\partial)/(\partial x)(y^2e^{-x})	\frac{\partial\:}{\partial\:x}(y^{2}e^{-x})
(\partial)/(\partial x)((Ax^c+By^c)^{1/c})	\frac{\partial\:}{\partial\:x}((Ax^{c}+By^{c})^{\frac{1}{c}})
(\partial)/(\partial x)(sqrt((18)/(xy)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{18}{xy}})
integral from 1 to 6 of kx	\int\:_{1}^{6}kxdx
limit as x approaches-2 of (x^2-5)/(2-x)	\lim\:_{x\to\:-2}(\frac{x^{2}-5}{2-x})
integral from 0 to 1 of 6x	\int\:_{0}^{1}6xdx
area y=e^x,y=x^2-1,x=-1,x=1	area\:y=e^{x},y=x^{2}-1,x=-1,x=1
sum from n=1 to infinity of ne^{6n}	\sum\:_{n=1}^{\infty\:}ne^{6n}
(dy)/(dt)-(3/t)*y=2t^3e^{2t},y(1)=0	\frac{dy}{dt}-(\frac{3}{t})\cdot\:y=2t^{3}e^{2t},y(1)=0
derivative of 7/(sqrt(x))	derivative\:\frac{7}{\sqrt{x}}
y^{''}+y=(x^2+x)sin(x)	y^{\prime\:\prime\:}+y=(x^{2}+x)\sin(x)
derivative of 3sec(x)-7x	derivative\:3\sec(x)-7x
limit as x approaches 8 of (2+8)/(2(8))	\lim\:_{x\to\:8}(\frac{2+8}{2(8)})
sum from n=1 to infinity of 1/(n+2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n+2}
area x^2+y^2=6,x=y^2,y=0	area\:x^{2}+y^{2}=6,x=y^{2},y=0
implicit (dy)/(dx),x^3-3axy+y^3=0	implicit\:\frac{dy}{dx},x^{3}-3axy+y^{3}=0
limit as x approaches pi of sin(7x)	\lim\:_{x\to\:π}(\sin(7x))
integral from-2 to 2 of (3u+1)^2	\int\:_{-2}^{2}(3u+1)^{2}du
derivative of (x^2+2/(x^3+1))	\frac{d}{dx}(\frac{x^{2}+2}{x^{3}+1})
derivative of (3sqrt(x)+7x^2)	\frac{d}{dx}((3\sqrt{x}+7)x^{2})
limit as x approaches 2 of-x^4	\lim\:_{x\to\:2}(-x^{4})
integral from 0 to 4 of 3x^2	\int\:_{0}^{4}3x^{2}dx
derivative of (x+2(x+6)^3)	\frac{d}{dx}((x+2)(x+6)^{3})
(\partial)/(\partial x)(x^4y^5+9x^7y)	\frac{\partial\:}{\partial\:x}(x^{4}y^{5}+9x^{7}y)
(x^2+1)y^'+y^2+1=0	(x^{2}+1)y^{\prime\:}+y^{2}+1=0
y^'+3/t y=1-2t,y(3)=0	y^{\prime\:}+\frac{3}{t}y=1-2t,y(3)=0
derivative of sin(2x+y)	\frac{d}{dx}(\sin(2x+y))
y^{''}-3y^'=4t	y^{\prime\:\prime\:}-3y^{\prime\:}=4t
integral of 2e^7	\int\:2e^{7}dx
integral from-3 to-2 of (x+2)/(x^2+4x)	\int\:_{-3}^{-2}\frac{x+2}{x^{2}+4x}dx
integral of (pi-x)^2	\int\:(π-x)^{2}dx
y^{''}-y^'-2y=3e^{2x}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=3e^{2x}
integral from-2 to 2 of (3-(x^2-1))	\int\:_{-2}^{2}(3-(x^{2}-1))dx
integral of (x^{1/3})/(x^{2/3)}	\int\:\frac{x^{\frac{1}{3}}}{x^{\frac{2}{3}}}dx
derivative of f(x)=3x^2-4x+3	derivative\:f(x)=3x^{2}-4x+3
integral of 8x^7e^{4x^8}	\int\:8x^{7}e^{4x^{8}}dx
integral from 1 to 2 of 1/8 (2+2x-x^2)	\int\:_{1}^{2}\frac{1}{8}(2+2x-x^{2})dx
integral of (x^2)/((1+x^3))	\int\:\frac{x^{2}}{(1+x^{3})}dx
integral from 0 to 4/3 of pi(4-3x)^2	\int\:_{0}^{\frac{4}{3}}π(4-3x)^{2}dx
limit as z approaches 1/2 of (3z+1)/(2z-5)	\lim\:_{z\to\:\frac{1}{2}}(\frac{3z+1}{2z-5})
(\partial)/(\partial y)(8xe^{x^2+y^2})	\frac{\partial\:}{\partial\:y}(8xe^{x^{2}+y^{2}})
derivative of f(x)=sqrt(4x)	derivative\:f(x)=\sqrt{4x}
derivative of \sqrt[3]{ln(x})	\frac{d}{dx}(\sqrt[3]{\ln(x)})
integral of 4sec^3(x)	\int\:4\sec^{3}(x)dx
integral of (3t)/(sqrt(1-9t^4))	\int\:\frac{3t}{\sqrt{1-9t^{4}}}dt
integral of 3cos(3x)	\int\:3\cos(3x)dx
tangent of f(x)=5e^x+7x,\at x=0	tangent\:f(x)=5e^{x}+7x,\at\:x=0
(\partial)/(\partial t)(e^{2x}-xcos(t))	\frac{\partial\:}{\partial\:t}(e^{2x}-x\cos(t))
limit as x approaches 0.9 of x^2-1	\lim\:_{x\to\:0.9}(x^{2}-1)
tangent of y=13xe^x	tangent\:y=13xe^{x}
(dy)/(dx)-(2x^3y)/(x^4+3)=x^3	\frac{dy}{dx}-\frac{2x^{3}y}{x^{4}+3}=x^{3}
derivative of 2Ax+B	\frac{d}{dx}(2Ax+B)
derivative of x^6ln(5x)	\frac{d}{dx}(x^{6}\ln(5x))
derivative of 1/(sqrt(x^2+2y^2-5))	\frac{d}{dx}(\frac{1}{\sqrt{x^{2}+2y^{2}-5}})
derivative of f(x)=sqrt(5)x+sqrt(6x)	derivative\:f(x)=\sqrt{5}x+\sqrt{6x}
derivative of f(x)=sqrt(20x)	derivative\:f(x)=\sqrt{20x}
limit as x approaches 0 of (sin(13x))/x	\lim\:_{x\to\:0}(\frac{\sin(13x)}{x})
integral of (2900)/(1+0.25x)	\int\:\frac{2900}{1+0.25x}dx
tangent of f(x)= 1/(sqrt(4x)),\at x=9	tangent\:f(x)=\frac{1}{\sqrt{4x}},\at\:x=9
derivative of 5x-32sqrt(x)	\frac{d}{dx}(5x-32\sqrt{x})
integral of (5000q)/(25q+1500)	\int\:\frac{5000q}{25q+1500}dq
integral from 0 to 1 of 40x	\int\:_{0}^{1}40xdx
limit as x approaches 0 of+(6-1/(x^3))	\lim\:_{x\to\:0}(+(6-\frac{1}{x^{3}}))
sum from n=3 to infinity of (8/11)^{-n}	\sum\:_{n=3}^{\infty\:}(\frac{8}{11})^{-n}
integral of (t^2+\sqrt[4]{t})	\int\:(t^{2}+\sqrt[4]{t})dt
sum from n=1 to infinity of 1/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{n}}
(\partial)/(\partial y)(nsin(2(mx+ny)))	\frac{\partial\:}{\partial\:y}(n\sin(2(mx+ny)))
inverse oflaplace (30)/((10s+1)(s^2+4))	inverselaplace\:\frac{30}{(10s+1)(s^{2}+4)}
derivative of x^{x+2}	derivative\:x^{x+2}
derivative of (x^2-64/(x-8))	\frac{d}{dx}(\frac{x^{2}-64}{x-8})
derivative of f(x)=sqrt(3-x)	derivative\:f(x)=\sqrt{3-x}
limit as x approaches-1 of pi	\lim\:_{x\to\:-1}(π)

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