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Popular Calculus Problems

integral of (sqrt(x^2+1))	\int\:(\sqrt{x^{2}+1})dx
(d^2)/(dx^2)(6x^2+5x)	\frac{d^{2}}{dx^{2}}(6x^{2}+5x)
(t+1)dt-1/(y^2)dy=0	(t+1)dt-\frac{1}{y^{2}}dy=0
integral of (2w-5)/(w^2-3w+9/2)	\int\:\frac{2w-5}{w^{2}-3w+\frac{9}{2}}dx
area 2x+y^2=8,x=y	area\:2x+y^{2}=8,x=y
(\partial)/(\partial x)(6xy-2y^2)	\frac{\partial\:}{\partial\:x}(6xy-2y^{2})
integral of (x+7)/(x^2+3x+2)	\int\:\frac{x+7}{x^{2}+3x+2}dx
derivative of y= 1/(x-2)	derivative\:y=\frac{1}{x-2}
implicit (dy)/(dx),e^{(9xy)}=10x	implicit\:\frac{dy}{dx},e^{(9xy)}=10x
integral of 1/2 cos(2x)	\int\:\frac{1}{2}\cos(2x)dx
e^y(dy)/(dx)=2x	e^{y}\frac{dy}{dx}=2x
integral of 20y	\int\:20ydy
derivative of (tan(x)/(cos(x)))	\frac{d}{dx}(\frac{\tan(x)}{\cos(x)})
derivative of 3sec^2(3x)	\frac{d}{dx}(3\sec^{2}(3x))
derivative of x/(x^2+1)	derivative\:\frac{x}{x^{2}+1}
integral of (5+cot^2(x))	\int\:(5+\cot^{2}(x))dx
inverse oflaplace s/(s^2+2s)	inverselaplace\:\frac{s}{s^{2}+2s}
limit as x approaches infinity of 5+3/x	\lim\:_{x\to\:\infty\:}(5+\frac{3}{x})
integral of \sqrt[3]{3-4x^2}(-8x)	\int\:\sqrt[3]{3-4x^{2}}(-8x)dx
integral of 15tan^2(xse)c^3x	\int\:15\tan^{2}(xse)c^{3}x
derivative of xsin(x/2)	\frac{d}{dx}(x\sin(\frac{x}{2}))
sum from n=0 to infinity of n*sin(1/n)	\sum\:_{n=0}^{\infty\:}n\cdot\:\sin(\frac{1}{n})
(\partial)/(\partial x)(sec^2(xy))	\frac{\partial\:}{\partial\:x}(\sec^{2}(xy))
sum from n=1 to infinity of 3/(pi^n)	\sum\:_{n=1}^{\infty\:}\frac{3}{π^{n}}
derivative of x^{1/3}-x^{-2/3}	derivative\:x^{\frac{1}{3}}-x^{-\frac{2}{3}}
limit as x approaches+0 of 2x^2cos(5/x)	\lim\:_{x\to\:+0}(2x^{2}\cos(\frac{5}{x}))
(\partial)/(\partial x)(e^x-2-cos(xy))	\frac{\partial\:}{\partial\:x}(e^{x}-2-\cos(xy))
derivative of 3/(5+x)	\frac{d}{dx}(\frac{3}{5+x})
integral of 1/(sqrt(x)+4)	\int\:\frac{1}{\sqrt{x}+4}dx
y^'=(2cos(y))/(sin(y))	y^{\prime\:}=\frac{2\cos(y)}{\sin(y)}
limit as x approaches 0-of (x-1)/x	\lim\:_{x\to\:0-}(\frac{x-1}{x})
integral of (cos(2x))/(1+sin^2(2x))	\int\:\frac{\cos(2x)}{1+\sin^{2}(2x)}dx
limit as x approaches 0 of (cos(x^2))/(x^2)	\lim\:_{x\to\:0}(\frac{\cos(x^{2})}{x^{2}})
y^'=6+t-y	y^{\prime\:}=6+t-y
derivative of y=x*e^x	derivative\:y=x\cdot\:e^{x}
laplacetransform (t-1)(3(t-1)^2+9(t-1)+3)	laplacetransform\:(t-1)(3(t-1)^{2}+9(t-1)+3)
integral of 1/(sec(y))	\int\:\frac{1}{\sec(y)}dy
limit as x approaches 0 of x(sin(1/x))	\lim\:_{x\to\:0}(x(\sin(\frac{1}{x})))
(\partial)/(\partial x)(ln(y^2+x^2))	\frac{\partial\:}{\partial\:x}(\ln(y^{2}+x^{2}))
integral of 1 (e^{x^2}y)	\int\:\frac{d}{1}(e^{x^{2}}y)dx
integral of-3t^2cos(t)	\int\:-3t^{2}\cos(t)dt
(\partial)/(\partial x)(m/(x^ay^bz^c))	\frac{\partial\:}{\partial\:x}(\frac{m}{x^{a}y^{b}z^{c}})
(\partial)/(\partial x)(3/8 xy)	\frac{\partial\:}{\partial\:x}(\frac{3}{8}xy)
derivative of acos(bx+c+d)	\frac{d}{dx}(a\cos(bx+c)+d)
area 6x^2-2x,x^3-6x+3	area\:6x^{2}-2x,x^{3}-6x+3
f(x)=sqrt(3x+1)	f(x)=\sqrt{3x+1}
(\partial)/(\partial x)(2x^2+3y^2-4x-5)	\frac{\partial\:}{\partial\:x}(2x^{2}+3y^{2}-4x-5)
derivative of (x^2+5^5)	\frac{d}{dx}((x^{2}+5)^{5})
derivative of (x^2+6/x)	\frac{d}{dx}(\frac{x^{2}+6}{x})
derivative of (x^2+4x/((3x^3+2)^4))	\frac{d}{dx}(\frac{x^{2}+4x}{(3x^{3}+2)^{4}})
integral of (x+9)ln(x)	\int\:(x+9)\ln(x)dx
derivative of f(x)=(2x-5)^4(x^2+x+1)^5	derivative\:f(x)=(2x-5)^{4}(x^{2}+x+1)^{5}
integral of (t^2+2t+1)^4	\int\:(t^{2}+2t+1)^{4}dt
25y^{''}+3y=0	25y^{\prime\:\prime\:}+3y=0
integral from 0 to 4 of 2pix(8-x^{3/2})	\int\:_{0}^{4}2πx(8-x^{\frac{3}{2}})dx
integral from 2 to 3 of (33)/(sqrt(3-x))	\int\:_{2}^{3}\frac{33}{\sqrt{3-x}}dx
(dx)/(dt)=e^x*sin(t)	\frac{dx}{dt}=e^{x}\cdot\:\sin(t)
maclaurin sin((xpi)/4)	maclaurin\:\sin(\frac{xπ}{4})
limit as x approaches infinity of 1/0	\lim\:_{x\to\:\infty\:}(\frac{1}{0})
integral of (x^2)/(sqrt(100-x^2))	\int\:\frac{x^{2}}{\sqrt{100-x^{2}}}dx
laplacetransform te^{-3t}cos(5t)	laplacetransform\:te^{-3t}\cos(5t)
(\partial)/(\partial x)(ln(x+y+z))	\frac{\partial\:}{\partial\:x}(\ln(x+y+z))
integral of x^2-3x+2	\int\:x^{2}-3x+2dx
integral of ((x^2-x+5))/x	\int\:\frac{(x^{2}-x+5)}{x}dx
y^{''}-5/x y^'+8/(x^2)y=0	y^{\prime\:\prime\:}-\frac{5}{x}y^{\prime\:}+\frac{8}{x^{2}}y=0
7t(dy)/(dt)-3y=sqrt(t)	7t\frac{dy}{dt}-3y=\sqrt{t}
derivative of 3/((4x^2-1^4))	\frac{d}{dx}(\frac{3}{(4x^{2}-1)^{4}})
inverse oflaplace (20)/((s^2+4)(s-4))	inverselaplace\:\frac{20}{(s^{2}+4)(s-4)}
limit as x approaches 2 of tan((pix)/4)	\lim\:_{x\to\:2}(\tan(\frac{πx}{4}))
(\partial)/(\partial x)(ln((2xy)/(7z)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{2xy}{7z}))
tangent of f(x)=1\sqrt[3]{x},\at x=1	tangent\:f(x)=1\sqrt[3]{x},\at\:x=1
integral of (x+2)sin(x)	\int\:(x+2)\sin(x)dx
integral from-1 to 2 of (20-x^4)	\int\:_{-1}^{2}(20-x^{4})dx
y/(1-x^2y^2)dx+x/(1-x^2y^2)dy=0	\frac{y}{1-x^{2}y^{2}}dx+\frac{x}{1-x^{2}y^{2}}dy=0
integral of (2-3/(x^{10)})	\int\:(2-\frac{3}{x^{10}})dx
d/(dy)((x^3y-xy^3)/(x^2+y^2))	\frac{d}{dy}(\frac{x^{3}y-xy^{3}}{x^{2}+y^{2}})
integral of e^{x^{-1/2}}	\int\:e^{x^{-\frac{1}{2}}}dx
integral of x5^x	\int\:x5^{x}dx
integral from 0 to 1 of (8+x)/(1+x^2)	\int\:_{0}^{1}\frac{8+x}{1+x^{2}}dx
inverse oflaplace (5+s)/(s(s^2-5s+4))	inverselaplace\:\frac{5+s}{s(s^{2}-5s+4)}
derivative of 3/5	\frac{d}{dx}(\frac{3}{5})
derivative of (1+2x)/(1-2x)	derivative\:\frac{1+2x}{1-2x}
sum from n=9 to infinity of e^{3-6n}	\sum\:_{n=9}^{\infty\:}e^{3-6n}
(y^2-1)dx-(2y+xy)dy=0	(y^{2}-1)dx-(2y+xy)dy=0
tangent of y=x^2-3x+1	tangent\:y=x^{2}-3x+1
(\partial)/(\partial x)(4(x-y)e^{4y+4x^2})	\frac{\partial\:}{\partial\:x}(4(x-y)e^{4y+4x^{2}})
x^{''}+3x^'-10x=6e^{4t}	x^{\prime\:\prime\:}+3x^{\prime\:}-10x=6e^{4t}
(\partial)/(\partial x)(2yx^2-4)	\frac{\partial\:}{\partial\:x}(2yx^{2}-4)
derivative of sqrt(r^2-13x^2)	derivative\:\sqrt{r^{2}-13x^{2}}
y^'=3-2x-0.5y,y(0)=1	y^{\prime\:}=3-2x-0.5y,y(0)=1
derivative of (ln(x)^{sec(x)})	\frac{d}{dx}((\ln(x))^{\sec(x)})
(\partial)/(\partial y)(xy^2e^z)	\frac{\partial\:}{\partial\:y}(x\cdot\:y^{2}\cdot\:e^{z})
integral of 8/((x-5)(x+3))	\int\:\frac{8}{(x-5)(x+3)}dx
integral of e^x*ln(x)	\int\:e^{x}\cdot\:\ln(x)dx
(\partial)/(\partial y)(e^{xy}-(x+1)cos(y))	\frac{\partial\:}{\partial\:y}(e^{xy}-(x+1)\cos(y))
limit as x approaches 0 of (x^3+7x)/x	\lim\:_{x\to\:0}(\frac{x^{3}+7x}{x})
area y=x^2-5,y=4	area\:y=x^{2}-5,y=4
integral from 6 to 8 of (64)/((x-6)^3)	\int\:_{6}^{8}\frac{64}{(x-6)^{3}}dx
integral of xcos(3x+1)	\int\:x\cos(3x+1)dx
derivative of \sqrt[5]{ln(6-x^2})	\frac{d}{dx}(\sqrt[5]{\ln(6-x^{2})})

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