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Popular Calculus Problems

(dy)/(dx)=(y^2)/(x^3),y(1)=1	\frac{dy}{dx}=\frac{y^{2}}{x^{3}},y(1)=1
integral of x/(xsqrt(81x^2-81))	\int\:\frac{x}{x\sqrt{81x^{2}-81}}dx
derivative of (ln(2x+1)^{1/2})	\frac{d}{dx}((\ln(2x+1))^{\frac{1}{2}})
integral of tan^2(2x)sec^2(2x)	\int\:\tan^{2}(2x)\sec^{2}(2x)dx
derivative of 3x-5sqrt(x)	\frac{d}{dx}(3x-5\sqrt{x})
integral of x(x+7)^4	\int\:x(x+7)^{4}dx
(1+x^2)(dy)/(dx)-xy=0	(1+x^{2})\frac{dy}{dx}-xy=0
limit as t approaches a of ln(t)	\lim\:_{t\to\:a}(\ln(t))
integral of t(t^2+1)^7	\int\:t(t^{2}+1)^{7}dt
(dy)/(dx)=e^x	\frac{dy}{dx}=e^{x}
derivative of (ax+b/c)	\frac{d}{dx}(\frac{ax+b}{c})
integral of tan^2(t)an(t)	\int\:\tan^{2}(t)d\tan(t)
integral of sqrt(16-3x^2)	\int\:\sqrt{16-3x^{2}}dx
derivative of (1+7x^2(x-x^2))	\frac{d}{dx}((1+7x^{2})(x-x^{2}))
integral from-5 to 5 of x(25-x^2)	\int\:_{-5}^{5}x(25-x^{2})dx
(\partial)/(\partial x)(2ye^{2xy})	\frac{\partial\:}{\partial\:x}(2ye^{2xy})
derivative of f(x)= x/(1-ln(x-6))	derivative\:f(x)=\frac{x}{1-\ln(x-6)}
2x+2y(dy)/(dx)=0	2x+2y\frac{dy}{dx}=0
integral from 0 to 5r of 2(25r^2-y^2)	\int\:_{0}^{5r}2(25r^{2}-y^{2})dy
integral of 1/(y^3+1)	\int\:\frac{1}{y^{3}+1}dy
integral of (10x^2-9x+20)/(x^3+4x)	\int\:\frac{10x^{2}-9x+20}{x^{3}+4x}dx
xy^'+xy-y^'-2y=0	xy^{\prime\:}+xy-y^{\prime\:}-2y=0
integral of-2tan(2x)	\int\:-2\tan(2x)dx
x^2y^'+xy=7	x^{2}y^{\prime\:}+xy=7
limit as x approaches 1+of x^2+2x	\lim\:_{x\to\:1+}(x^{2}+2x)
limit as x approaches 0 of ((sin(6x)))/x	\lim\:_{x\to\:0}(\frac{(\sin(6x))}{x})
integral of (sqrt(x^2+9))/x	\int\:\frac{\sqrt{x^{2}+9}}{x}dx
derivative of 1/9 (x^2+6^{3/2})	\frac{d}{dx}(\frac{1}{9}(x^{2}+6)^{\frac{3}{2}})
y^'+1/x y=9x^2	y^{\prime\:}+\frac{1}{x}y=9x^{2}
(\partial)/(\partial x)(x^2ln(y+1))	\frac{\partial\:}{\partial\:x}(x^{2}\ln(y+1))
area 3sqrt(x),x	area\:3\sqrt{x},x
integral of (sec^2(3x))/(1+tan(3x))	\int\:\frac{\sec^{2}(3x)}{1+\tan(3x)}dx
slope of y=x^2-3x-5,(2,-7)	slope\:y=x^{2}-3x-5,(2,-7)
tangent of f(x)=3x^2-12x+1,(0,1)	tangent\:f(x)=3x^{2}-12x+1,(0,1)
derivative of (x^3/3-2x^2-5x)	\frac{d}{dx}(\frac{x^{3}}{3}-2x^{2}-5x)
tangent of f(x)=x^2-4,\at x=5	tangent\:f(x)=x^{2}-4,\at\:x=5
sum from n=0 to infinity of 3^{-2n}	\sum\:_{n=0}^{\infty\:}3^{-2n}
derivative of ln(3xe^{-x})	\frac{d}{dx}(\ln(3xe^{-x}))
area 15-x^2,-6x-1,[-4,-1]	area\:15-x^{2},-6x-1,[-4,-1]
integral of 9/((x+1)^2)	\int\:\frac{9}{(x+1)^{2}}dx
integral of (1-2x)/((x+1)(x-5))	\int\:\frac{1-2x}{(x+1)(x-5)}dx
derivative of xe^{xy}+2xy+1/x	\frac{d}{dx}(xe^{xy}+2xy+\frac{1}{x})
y^'-e^y-2xe^y=0	y^{\prime\:}-e^{y}-2xe^{y}=0
derivative of y=sin(tan(7x))	derivative\:y=\sin(\tan(7x))
(\partial)/(\partial x)(4x(3+y)^{-1})	\frac{\partial\:}{\partial\:x}(4x(3+y)^{-1})
integral of 56cos(8x-5)	\int\:56\cos(8x-5)dx
integral from 0 to infinity of (xe^{-x})	\int\:_{0}^{\infty\:}(xe^{-x})dx
integral of e^{2x+e^{2x}}	\int\:e^{2x+e^{2x}}dx
(\partial)/(\partial x)(y^2-xy)	\frac{\partial\:}{\partial\:x}(y^{2}-xy)
implicit (dy)/(dx),y=ln(x)	implicit\:\frac{dy}{dx},y=\ln(x)
(d^2)/(dx^2)((x^2+2)^7)	\frac{d^{2}}{dx^{2}}((x^{2}+2)^{7})
limit as x approaches-1-of 3/(x+1)	\lim\:_{x\to\:-1-}(\frac{3}{x+1})
f^'(x)= 5/(6x^5)	f^{\prime\:}(x)=\frac{5}{6x^{5}}
integral of (sin(x)+cos(x))/(tan(x))	\int\:\frac{\sin(x)+\cos(x)}{\tan(x)}dx
integral of 6x^5e^{8x^6}	\int\:6x^{5}e^{8x^{6}}dx
derivative of (3x^2-9x+13)/(3x+4)	derivative\:\frac{3x^{2}-9x+13}{3x+4}
integral of-x^2+4x-3	\int\:-x^{2}+4x-3dx
derivative of 9tan(x)	\frac{d}{dx}(9\tan(x))
(\partial)/(\partial x)((10x)/(1+x^2-y))	\frac{\partial\:}{\partial\:x}(\frac{10x}{1+x^{2}-y})
(\partial)/(\partial y)(y/2)	\frac{\partial\:}{\partial\:y}(\frac{y}{2})
derivative of f(x)=3x^2-1	derivative\:f(x)=3x^{2}-1
(dy)/(dx)=x+6y,y(0)=2	\frac{dy}{dx}=x+6y,y(0)=2
tangent of f(x)=(4x+5)/(x-1),(2,13)	tangent\:f(x)=\frac{4x+5}{x-1},(2,13)
area 2sqrt(x),2x	area\:2\sqrt{x},2x
sum from n=1 to infinity of (1/2)^{2n-1}	\sum\:_{n=1}^{\infty\:}(\frac{1}{2})^{2n-1}
(\partial)/(\partial x)(xz)	\frac{\partial\:}{\partial\:x}(xz)
derivative of 2x^3+3x^2-12x+3	derivative\:2x^{3}+3x^{2}-12x+3
derivative of f(x)=(x^2-4)^2	derivative\:f(x)=(x^{2}-4)^{2}
derivative of 3xe^{-kx}	derivative\:3xe^{-kx}
(d^2)/(dx^2)((x^2)/((1+x)))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{(1+x)})
limit as x approaches 6 of (x-6)/(x-6)	\lim\:_{x\to\:6}(\frac{x-6}{x-6})
integral of sqrt(4x-x^2)	\int\:\sqrt{4x-x^{2}}dx
derivative of P(x)=x(x-8)(x+5)	derivative\:P(x)=x(x-8)(x+5)
integral from 0 to 2 of (x/((3-x)^2))	\int\:_{0}^{2}(\frac{x}{(3-x)^{2}})dx
y^'=3y+xe^x	y^{\prime\:}=3y+xe^{x}
integral of 2arctan(y/x)	\int\:2\arctan(\frac{y}{x})dx
integral of (x^3+3x^2+5x+4)/(x^2+3x+2)	\int\:\frac{x^{3}+3x^{2}+5x+4}{x^{2}+3x+2}dx
inverse oflaplace ((10))/(5*s^2+7s)	inverselaplace\:\frac{(10)}{5\cdot\:s^{2}+7s}
integral of (4y^2-7y-12)/(y(y+2)(y-3))	\int\:\frac{4y^{2}-7y-12}{y(y+2)(y-3)}dy
derivative of cy^{-7}	derivative\:cy^{-7}
integral of 3e^{x/3}	\int\:3e^{\frac{x}{3}}dx
integral of 1/(2x+1)+1/(sqrt(1-x))	\int\:\frac{1}{2x+1}+\frac{1}{\sqrt{1-x}}dx
integral of sec^2(x)+1	\int\:\sec^{2}(x)+1dx
y^'=(2x+y)^2	y^{\prime\:}=(2x+y)^{2}
y^{''}+7y+10=0,y(0)=3,y^'(0)=18	y^{\prime\:\prime\:}+7y+10=0,y(0)=3,y^{\prime\:}(0)=18
d/(ds)((6s^3+28s^2+38s+15)/((s+1)^2))	\frac{d}{ds}(\frac{6s^{3}+28s^{2}+38s+15}{(s+1)^{2}})
derivative of 2x^3-9x^2+12x-3	\frac{d}{dx}(2x^{3}-9x^{2}+12x-3)
f(x)= 1/(x^8)	f(x)=\frac{1}{x^{8}}
derivative of ln(ln(15x))	\frac{d}{dx}(\ln(\ln(15x)))
derivative of tsin(pit)	derivative\:t\sin(πt)
integral from 3 to 4.5 of x/8	\int\:_{3}^{4.5}\frac{x}{8}dx
integral of (x^3)/(x^3+1)	\int\:\frac{x^{3}}{x^{3}+1}dx
integral of (4+sqrt(x))/(x^2)	\int\:\frac{4+\sqrt{x}}{x^{2}}dx
(dq)/(dt)=5-5q	\frac{dq}{dt}=5-5q
derivative of y=log_{2}(x)*log_{5}(x)	derivative\:y=\log_{2}(x)\cdot\:\log_{5}(x)
limit as x approaches 2-of 1/(x^2-4)	\lim\:_{x\to\:2-}(\frac{1}{x^{2}-4})
inverse oflaplace (e^{-4s})/((s+2)^3)	inverselaplace\:\frac{e^{-4s}}{(s+2)^{3}}
limit as x approaches 0+of (2x)/(x^2)	\lim\:_{x\to\:0+}(\frac{2x}{x^{2}})
derivative of (5-4x^2+x^5/(x^3))	\frac{d}{dx}(\frac{5-4x^{2}+x^{5}}{x^{3}})
integral of (36)/(36+e^x)	\int\:\frac{36}{36+e^{x}}dx

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