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Popular Calculus Problems

integral from 4 to 9 of 3sqrt(x)	\int\:_{4}^{9}3\sqrt{x}dx
integral of 3x^3cos(x)	\int\:3x^{3}\cos(x)dx
tangent of f(x)=x^2-5x+5,\at x=0	tangent\:f(x)=x^{2}-5x+5,\at\:x=0
integral of x^2+4x	\int\:x^{2}+4xdx
y^{''}+y=-sin(2x)	y^{\prime\:\prime\:}+y=-\sin(2x)
d/(dy)(arctan(x/y))	\frac{d}{dy}(\arctan(\frac{x}{y}))
derivative of x/((1+4x^2))	\frac{d}{dx}(\frac{x}{(1+4x)^{2}})
integral of (12)/(4x^2+5x+1)	\int\:\frac{12}{4x^{2}+5x+1}dx
integral of (x+3)^2(3-x)^7	\int\:(x+3)^{2}(3-x)^{7}dx
limit as x approaches 9 of x	\lim\:_{x\to\:9}(x)
derivative of f(x)=sqrt(x^2-x-2)	derivative\:f(x)=\sqrt{x^{2}-x-2}
derivative of (6x^2-12x+12e^x)	\frac{d}{dx}((6x^{2}-12x+12)e^{x})
derivative of (6x^2+4x+4)/(sqrt(x))	derivative\:\frac{6x^{2}+4x+4}{\sqrt{x}}
integral of (x^2+2x+1)^5(x+1)	\int\:(x^{2}+2x+1)^{5}(x+1)dx
integral from-1 to 4 of 4-x^2+3x	\int\:_{-1}^{4}4-x^{2}+3xdx
integral of (1/3)x^3	\int\:(\frac{1}{3})x^{3}dx
limit as x approaches 1 of (x+1)/(x-1)	\lim\:_{x\to\:1}(\frac{x+1}{x-1})
integral of 5/(2(2x-3)^2)	\int\:\frac{5}{2(2x-3)^{2}}dx
derivative of (-x^2-3/((x^2-3)^2))	\frac{d}{dx}(\frac{-x^{2}-3}{(x^{2}-3)^{2}})
slope of 6x^2+3xy+y^2=16,(1,2)	slope\:6x^{2}+3xy+y^{2}=16,(1,2)
integral from 1 to 8 of pi(sqrt(x-1))^2	\int\:_{1}^{8}π(\sqrt{x-1})^{2}dx
derivative of sqrt(2)dx	\frac{d}{dx}(\sqrt{2}dx)
integral of 1/(e^{2x)+4}	\int\:\frac{1}{e^{2x}+4}dx
y^{''}+4y^'+3y=e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=e^{-x}
integral of (cos(x))e^{sin(x)}	\int\:(\cos(x))e^{\sin(x)}dx
(\partial)/(\partial x)(4xy-5x^2y)	\frac{\partial\:}{\partial\:x}(4xy-5x^{2}y)
derivative of sqrt(3)sec(x)	\frac{d}{dx}(\sqrt{3}\sec(x))
area y=1,y=\sqrt[4]{x},[0,1]	area\:y=1,y=\sqrt[4]{x},[0,1]
tangent of y=3x^2+2	tangent\:y=3x^{2}+2
derivative of ((5^x/(x^5))^{sin(x^5)})	\frac{d}{dx}((\frac{5^{x}}{x^{5}})^{\sin(x^{5})})
limit as x approaches-2 of 2016	\lim\:_{x\to\:-2}(2016)
derivative of f(x)=(2x^2tan(x))/(sec(x))	derivative\:f(x)=\frac{2x^{2}\tan(x)}{\sec(x)}
limit as x approaches 1 of x+sqrt(x)	\lim\:_{x\to\:1}(x+\sqrt{x})
(1-x)^'	(1-x)^{\prime\:}
limit as x approaches 1/2 of x^4	\lim\:_{x\to\:\frac{1}{2}}(x^{4})
t^2y^'+y^'=ty	t^{2}\cdot\:y^{\prime\:}+y^{\prime\:}=t\cdot\:y
derivative of (2x-3/(2x+3))	\frac{d}{dx}(\frac{2x-3}{2x+3})
y^{'''}+y^{''}-y^'-y=4e^x	y^{\prime\:\prime\:\prime\:}+y^{\prime\:\prime\:}-y^{\prime\:}-y=4e^{x}
derivative of sin^2(x-3)	\frac{d}{dx}(\sin^{2}(x)-3)
(\partial)/(\partial x)(e^{5x}cos(7y))	\frac{\partial\:}{\partial\:x}(e^{5x}\cos(7y))
derivative of (2x+3/(5x+4))	\frac{d}{dx}(\frac{2x+3}{5x+4})
derivative of 2e^{(x-5})	\frac{d}{dx}(2e^{(x-5)})
integral of ((x^2+2))/(x+1)	\int\:\frac{(x^{2}+2)}{x+1}dx
derivative of (2x^2-3^3)	\frac{d}{dx}((2x^{2}-3)^{3})
derivative of y= 2/((4x-3)^{1/2)}	derivative\:y=\frac{2}{(4x-3)^{\frac{1}{2}}}
tangent of f(x)=(1+2x)^2	tangent\:f(x)=(1+2x)^{2}
derivative of (4x+5)^3	derivative\:(4x+5)^{3}
limit as x approaches pi/2 of-cot(2x)	\lim\:_{x\to\:\frac{π}{2}}(-\cot(2x))
derivative of 12tan(cosh(e^{4x}))	\frac{d}{dx}(12\tan(\cosh(e^{4x})))
integral of (e^{-x}-e^3)(e^x-e^{-5})	\int\:(e^{-x}-e^{3})(e^{x}-e^{-5})dx
derivative of y=e^{7tsin(2t)}	derivative\:y=e^{7t\sin(2t)}
integral of (x^{3/2}+4x+6)	\int\:(x^{\frac{3}{2}}+4x+6)dx
integral of 1/4 e^{-x/4}	\int\:\frac{1}{4}e^{-\frac{x}{4}}dx
tangent of y=f(x),\at x=2	tangent\:y=f(x),\at\:x=2
limit as x approaches-2-of (-3)/(x^2-4)	\lim\:_{x\to\:-2-}(\frac{-3}{x^{2}-4})
sum from n=1 to infinity of 1/(n^3+2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{3}+2}
derivative of f(x)=x^2(1-7x)	derivative\:f(x)=x^{2}(1-7x)
integral of 2/(x(x^2+25))	\int\:\frac{2}{x(x^{2}+25)}dx
cos^2(x)sin(x)y^'+cos^3(x)y=2	\cos^{2}(x)\sin(x)y^{\prime\:}+\cos^{3}(x)y=2
integral from 0 to 3 of 2pix(3-sqrt(x))	\int\:_{0}^{3}2πx(3-\sqrt{x})dx
(\partial)/(\partial x)(4ln(xy)-(x+y)^2+5)	\frac{\partial\:}{\partial\:x}(4\ln(xy)-(x+y)^{2}+5)
derivative of f(x)=((3x+2))/((3x-2))	derivative\:f(x)=\frac{(3x+2)}{(3x-2)}
integral of (xln(x))	\int\:(x\ln(x))dx
integral of (x+1)y^2*sin((xy)/3)	\int\:(x+1)y^{2}\cdot\:\sin(\frac{xy}{3})dx
limit as x approaches 0-of g(t)	\lim\:_{x\to\:0-}(g(t))
derivative of ln(xy^2)	\frac{d}{dx}(\ln(xy^{2}))
y^{''}+4y=2sin(2x)	y^{\prime\:\prime\:}+4y=2\sin(2x)
integral of 1/(4x^2+9)	\int\:\frac{1}{4x^{2}+9}dx
derivative of 1/(6x^2)	\frac{d}{dx}(\frac{1}{6x^{2}})
integral of 1/((x^2-4x+4)(x^2-5x+6))	\int\:\frac{1}{(x^{2}-4x+4)(x^{2}-5x+6)}dx
integral of 1/(3+sqrt(2x))	\int\:\frac{1}{3+\sqrt{2x}}dx
integral of-1sin^3(x)cos^2(x)	\int\:-1\sin^{3}(x)\cos^{2}(x)dx
limit as x approaches infinity of x	\lim\:_{x\to\:\infty\:}(x)
integral of x(tan(x))^2	\int\:x(\tan(x))^{2}dx
area x^2+1,3-x,x=0	area\:x^{2}+1,3-x,x=0
derivative of ((tan(x)/x)^2)	\frac{d}{dx}((\frac{\tan(x)}{x})^{2})
integral of (x-6)/((x+3)^2+36)	\int\:\frac{x-6}{(x+3)^{2}+36}dx
sum from n=1 to infinity of nln(2)	\sum\:_{n=1}^{\infty\:}n\ln(2)
integral of sin^2(v)cos^3(v)	\int\:\sin^{2}(v)\cos^{3}(v)dv
derivative of (sin(x)(cos(x)))	\frac{d}{dx}((\sin(x))(\cos(x)))
implicit (dy)/(dx),xy=15	implicit\:\frac{dy}{dx},xy=15
(\partial)/(\partial x)(2sin(x^2+y^2))	\frac{\partial\:}{\partial\:x}(2\sin(x^{2}+y^{2}))
tangent of f(x)=(sqrt(5))^x,\at x=4	tangent\:f(x)=(\sqrt{5})^{x},\at\:x=4
integral of x^2sqrt(1-x^3)	\int\:x^{2}\sqrt{1-x^{3}}dx
d/(dθ)(8sin(θ))	\frac{d}{dθ}(8\sin(θ))
integral of 17x^3e^x	\int\:17x^{3}e^{x}dx
(\partial)/(\partial x)((4y)/(x^5))	\frac{\partial\:}{\partial\:x}(\frac{4y}{x^{5}})
d/(d{x)}(ln(16-4{x}^2-4{y}^2-{z}^2))	\frac{d}{d{x}}(\ln(16-4{x}^{2}-4{y}^{2}-{z}^{2}))
(\partial)/(\partial x)(3y-3x^2)	\frac{\partial\:}{\partial\:x}(3y-3x^{2})
limit as x approaches 0-of 1/(sin(x))	\lim\:_{x\to\:0-}(\frac{1}{\sin(x)})
derivative of sqrt(-5+9x)	derivative\:\sqrt{-5+9x}
(dy)/(dt)=2ty^2	\frac{dy}{dt}=2ty^{2}
integral of (x-2pi)	\int\:(x-2π)dx
integral of (sin^4(x)+cos^4(x))	\int\:(\sin^{4}(x)+\cos^{4}(x))dx
(dy}{dx}=\frac{2y)/x+y	\frac{dy}{dx}=\frac{2y}{x}+y
d/(ds)(s/(s^2+k^2))	\frac{d}{ds}(\frac{s}{s^{2}+k^{2}})
limit as x approaches a of (x-1)^2	\lim\:_{x\to\:a}((x-1)^{2})
integral from 0 to 1 of x^{-2/3}	\int\:_{0}^{1}x^{-\frac{2}{3}}dx
integral of (x^2-3x+5)/(sqrt(x))	\int\:\frac{x^{2}-3x+5}{\sqrt{x}}dx
(\partial)/(\partial x)((x-3)^2+(y-4)^2)	\frac{\partial\:}{\partial\:x}((x-3)^{2}+(y-4)^{2})

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