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Popular Calculus Problems

integral of 1/(u^2+3)	\int\:\frac{1}{u^{2}+3}du
(dx}{dy}=\frac{y^3-3x)/y	\frac{dx}{dy}=\frac{y^{3}-3x}{y}
sum from n=1 to infinity of 4/(2n)	\sum\:_{n=1}^{\infty\:}\frac{4}{2n}
(d^3)/(dx^3)(6/(x^2))	\frac{d^{3}}{dx^{3}}(\frac{6}{x^{2}})
integral of (y^2cos(x)-3x^2y-2x)	\int\:(y^{2}\cos(x)-3x^{2}y-2x)dx
(\partial)/(\partial z)(ln(xy))	\frac{\partial\:}{\partial\:z}(\ln(xy))
area x^3-4x^2,2x^2-8x	area\:x^{3}-4x^{2},2x^{2}-8x
inverse oflaplace 1/((s^2+1)(s^2+3s))	inverselaplace\:\frac{1}{(s^{2}+1)(s^{2}+3s)}
integral of (24x^3-48x^2+7)/(x^2-2x)	\int\:\frac{24x^{3}-48x^{2}+7}{x^{2}-2x}dx
(2xln(x)+x^2-1)^'	(2x\ln(x)+x^{2}-1)^{\prime\:}
(\partial)/(\partial x)(u(x))	\frac{\partial\:}{\partial\:x}(u(x))
integral of (y^2e^{xy})	\int\:(y^{2}e^{xy})dx
(\partial)/(\partial x)((x-2y)/(x+2y))	\frac{\partial\:}{\partial\:x}(\frac{x-2y}{x+2y})
(\partial)/(\partial x)(ln(x+2ct))	\frac{\partial\:}{\partial\:x}(\ln(x+2ct))
derivative of f(x)=186.5	derivative\:f(x)=186.5
integral of 2/(xln(6x))	\int\:\frac{2}{x\ln(6x)}dx
integral of 1/(xsqrt(6x+49))	\int\:\frac{1}{x\sqrt{6x+49}}dx
(2y^2+6x)dx+(2xy)dy=0	(2y^{2}+6x)dx+(2xy)dy=0
integral of cot^3(x)csc^2(x)	\int\:\cot^{3}(x)\csc^{2}(x)dx
derivative of 2x^2cos(x)cot(x)	derivative\:2x^{2}\cos(x)\cot(x)
derivative of f(x)=sqrt(5)	derivative\:f(x)=\sqrt{5}
derivative of cos(9sin(x))	\frac{d}{dx}(\cos(9\sin(x)))
derivative of (tan^2(x-x^2)^3)	\frac{d}{dx}((\tan^{2}(x)-x^{2})^{3})
integral from 0 to 1 of (1+x)/(1+2x)	\int\:_{0}^{1}\frac{1+x}{1+2x}dx
taylor (e^x)/(1+x)	taylor\:\frac{e^{x}}{1+x}
(dy)/(dx)+ay+b=0	\frac{dy}{dx}+ay+b=0
limit as x approaches 3-of (x+3)/2	\lim\:_{x\to\:3-}(\frac{x+3}{2})
slope of (2,5),(7,3)	slope\:(2,5),(7,3)
integral of (x^{1/2}+3x+2)	\int\:(x^{\frac{1}{2}}+3x+2)dx
limit as θ approaches 0 of θcos(θ)	\lim\:_{θ\to\:0}(θ\cos(θ))
integral of ((ln^2(3x)))/x	\int\:\frac{(\ln^{2}(3x))}{x}dx
f(x)= x/(1+x^2)	f(x)=\frac{x}{1+x^{2}}
integral from 0 to 1 of (xsqrt(x^2+1))	\int\:_{0}^{1}(x\sqrt{x^{2}+1})dx
derivative of (120/((1-x)^6))	\frac{d}{dx}(\frac{120}{(1-x)^{6}})
tangent of ((x+3))/(2x+1)	tangent\:\frac{(x+3)}{2x+1}
derivative of (3x^2(x^{1/2}))	\frac{d}{dx}((3x^{2})(x^{\frac{1}{2}}))
integral from 2 to infinity of 5x^{-2}	\int\:_{2}^{\infty\:}5x^{-2}dx
integral of xsqrt(5+2x^2)	\int\:x\sqrt{5+2x^{2}}dx
a^2dx=xsqrt(x^2-a^2)dy	a^{2}dx=x\sqrt{x^{2}-a^{2}}dy
area y=3x,y=9,y= 1/4 x^2	area\:y=3x,y=9,y=\frac{1}{4}x^{2}
integral of (x^3+2)^83x^2	\int\:(x^{3}+2)^{8}3x^{2}dx
derivative of sqrt(5x-\sqrt{x)}	\frac{d}{dx}(\sqrt{5x-\sqrt{x}})
limit as x approaches-pi/2 of csc(x)	\lim\:_{x\to\:-\frac{π}{2}}(\csc(x))
derivative of ln(4x-x^2-3)	derivative\:\ln(4x-x^{2}-3)
integral of sin(2x)sin(cos(2x))	\int\:\sin(2x)\sin(\cos(2x))dx
(\partial)/(\partial x)(sin(3x+4y))	\frac{\partial\:}{\partial\:x}(\sin(3x+4y))
derivative of (4x+7)^2	derivative\:(4x+7)^{2}
derivative of (sqrt(x+4)/(sqrt(x-1)))	\frac{d}{dx}(\frac{\sqrt{x+4}}{\sqrt{x-1}})
derivative of ln(5x+2)	\frac{d}{dx}(\ln(5x+2))
derivative of sqrt(x+12)	derivative\:\sqrt{x+12}
(\partial)/(\partial x)(-(2y)/(3+2x))	\frac{\partial\:}{\partial\:x}(-\frac{2y}{3+2x})
integral of (-28)/(x^2sqrt(x^2+25))	\int\:\frac{-28}{x^{2}\sqrt{x^{2}+25}}dx
limit as x approaches 10 of 1/(x-10)	\lim\:_{x\to\:10}(\frac{1}{x-10})
sum from n=1 to infinity of (-3/2)^n	\sum\:_{n=1}^{\infty\:}(-\frac{3}{2})^{n}
integral from-1 to 0 of x-2	\int\:_{-1}^{0}x-2dx
integral of 1/(x(x+1)(x-2))	\int\:\frac{1}{x(x+1)(x-2)}dx
(dy)/(dx)= y/x+y^4	\frac{dy}{dx}=\frac{y}{x}+y^{4}
(x^2+3)(dy)/(dx)=xy	(x^{2}+3)\frac{dy}{dx}=xy
integral of (2x^3+4x^2-5)/(x+3)	\int\:\frac{2x^{3}+4x^{2}-5}{x+3}dx
derivative of (x^2/(x^2+1))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+1})
derivative of 3x^4-4x^3-12x^2+5	\frac{d}{dx}(3x^{4}-4x^{3}-12x^{2}+5)
derivative of sin((pix/9))	\frac{d}{dx}(\sin(\frac{πx}{9}))
(\partial)/(\partial x)(xye^{-8y})	\frac{\partial\:}{\partial\:x}(xye^{-8y})
d/(dt)(4cos(t))	\frac{d}{dt}(4\cos(t))
derivative of (2x^2/(x-3))	\frac{d}{dx}(\frac{2x^{2}}{x-3})
integral of 1/(x^{1.4)}	\int\:\frac{1}{x^{1.4}}dx
integral of (y^2+26y+169)/((y^2+169)^2)	\int\:\frac{y^{2}+26y+169}{(y^{2}+169)^{2}}dy
integral of (cos(2x)+sin(2x))^2	\int\:(\cos(2x)+\sin(2x))^{2}dx
simplify ((x^3-5x+186))/(x^2-x-42)	simplify\:\frac{(x^{3}-5x+186)}{x^{2}-x-42}
area sin(x),cos(x),(-pi)/(30), 25/12	area\:\sin(x),\cos(x),\frac{-π}{30},\frac{25}{12}
y^{''}+y^'+1.25y=0,y(0)=3,y^'(0)=1	y^{\prime\:\prime\:}+y^{\prime\:}+1.25y=0,y(0)=3,y^{\prime\:}(0)=1
integral of 23sec^{-2}(xta)n^3x	\int\:23\sec^{-2}(xta)n^{3}xdx
derivative of \sqrt[5]{x^2}-2/x	derivative\:\sqrt[5]{x^{2}}-\frac{2}{x}
integral of (x*e^x)/((x+1)^2)	\int\:\frac{x\cdot\:e^{x}}{(x+1)^{2}}dx
derivative of (x^4+1/(x^2+1))	\frac{d}{dx}(\frac{x^{4}+1}{x^{2}+1})
(\partial)/(\partial x)(y(e^{x^2-xy}))	\frac{\partial\:}{\partial\:x}(y(e^{x^{2}-xy}))
integral of 6sin(6x)	\int\:6\sin(6x)dx
(\partial)/(\partial x)(e^6)	\frac{\partial\:}{\partial\:x}(e^{6})
integral of (x^2)/(sqrt(x^6+4))	\int\:\frac{x^{2}}{\sqrt{x^{6}+4}}dx
derivative of f(x)=-5csc(x)+sec(x)	derivative\:f(x)=-5\csc(x)+\sec(x)
(\partial)/(\partial x)(4-sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(4-\sqrt{x^{2}+y^{2}})
integral of 1/7 x^{-3/7}	\int\:\frac{1}{7}x^{-\frac{3}{7}}dx
limit as x approaches 5 of 5x(5-x)	\lim\:_{x\to\:5}(5x(5-x))
y^'-y=2te^2t	y^{\prime\:}-y=2te^{2}t
derivative of cos(x+x^2sin(x))	\frac{d}{dx}(\cos(x)+x^{2}\sin(x))
(\partial)/(\partial y)(xe^{5y})	\frac{\partial\:}{\partial\:y}(xe^{5y})
derivative of (cos(x+2)^3(2x)^{-3x})	\frac{d}{dx}((\cos(x)+2)^{3}(2x)^{-3x})
sum from n=1 to infinity of ((-1)^nx^n)/(\sqrt[3]{n)}	\sum\:_{n=1}^{\infty\:}\frac{(-1)^{n}x^{n}}{\sqrt[3]{n}}
derivative of f(x)= 9/(x^3)	derivative\:f(x)=\frac{9}{x^{3}}
derivative of ln(x-2x)	\frac{d}{dx}(\ln(x)-2x)
laplacetransform tsin(3t)+2tcos(t)	laplacetransform\:t\sin(3t)+2t\cos(t)
tangent of f(x)=(2x+1)/(x+2),\at x=1	tangent\:f(x)=\frac{2x+1}{x+2},\at\:x=1
(\partial)/(\partial x)(-(5x^3+5xy^2))	\frac{\partial\:}{\partial\:x}(-(5x^{3}+5xy^{2}))
(\partial)/(\partial h)(x^2h)	\frac{\partial\:}{\partial\:h}(x^{2}h)
maclaurin 1/(x+2)	maclaurin\:\frac{1}{x+2}
integral of (x^2-2)/(x^2+x)	\int\:\frac{x^{2}-2}{x^{2}+x}dx
(x+2)(dy)/(dx)+y=ln(x),y(1)=20	(x+2)\frac{dy}{dx}+y=\ln(x),y(1)=20
area x,x^2,0,1	area\:x,x^{2},0,1
(\partial)/(\partial y)(x^2y+y^2z)	\frac{\partial\:}{\partial\:y}(x^{2}y+y^{2}z)
derivative of 1/(x(x+1))	\frac{d}{dx}(\frac{1}{x(x+1)})

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