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Popular Calculus Problems

integral of x^r	\int\:x^{r}dx
derivative of (x^2-6x+12)/(x-4)	derivative\:\frac{x^{2}-6x+12}{x-4}
y^'+y=e^{-x}sqrt(x)	y^{\prime\:}+y=e^{-x}\sqrt{x}
integral of (2x^2+7x+2)/((x^2+1)^2)	\int\:\frac{2x^{2}+7x+2}{(x^{2}+1)^{2}}dx
derivative of 3x^{2/3}-x	\frac{d}{dx}(3x^{\frac{2}{3}}-x)
derivative of (2x+1^{-1})	\frac{d}{dx}((2x+1)^{-1})
integral of (arcsin(sqrt(x)))/(sqrt(x))	\int\:\frac{\arcsin(\sqrt{x})}{\sqrt{x}}dx
y^{''}+16y^'+80y=0	y^{\prime\:\prime\:}+16y^{\prime\:}+80y=0
derivative of-x^3+3x^2+9x-1	\frac{d}{dx}(-x^{3}+3x^{2}+9x-1)
taylor e^{2x},-2	taylor\:e^{2x},-2
integral of 1/(-x^2+249x+250)	\int\:\frac{1}{-x^{2}+249x+250}dx
sum from n=0 to infinity of (-5)^n	\sum\:_{n=0}^{\infty\:}(-5)^{n}
integral from 0 to 1 of (1+4xy)	\int\:_{0}^{1}(1+4xy)dx
tangent of y=3+4x^2-2x^3,(2,3)	tangent\:y=3+4x^{2}-2x^{3},(2,3)
derivative of (4+csc(x)/(8-csc(x)))	\frac{d}{dx}(\frac{4+\csc(x)}{8-\csc(x)})
integral of 4x^3ln(x)	\int\:4x^{3}\ln(x)dx
derivative of cx+ln(cos(x))	\frac{d}{dx}(cx+\ln(\cos(x)))
y^'+ry^{''}=0	y^{\prime\:}+ry^{\prime\:\prime\:}=0
derivative of (x^2+2^{-5}(cos(x)))	\frac{d}{dx}((x^{2}+2)^{-5}(\cos(x)))
integral from 1200 to 1210 of 0.1x^2	\int\:_{1200}^{1210}0.1x^{2}dx
derivative of ((x^2+1)/(x^2-1))^7	derivative\:(\frac{x^{2}+1}{x^{2}-1})^{7}
derivative of (x^3-3x(2x^2+3x+5))	\frac{d}{dx}((x^{3}-3x)(2x^{2}+3x+5))
sum from n=0 to infinity of 1/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{3^{n}}
f(x)=\sqrt[7]{ln(x)}	f(x)=\sqrt[7]{\ln(x)}
integral of (15)/(25+x^2)	\int\:\frac{15}{25+x^{2}}dx
limit as x approaches-2 of 2/(x+2)	\lim\:_{x\to\:-2}(\frac{2}{x+2})
integral of x^5(x^6-10)^4	\int\:x^{5}(x^{6}-10)^{4}dx
(x^2+4)dy=(2x-8y)dx	(x^{2}+4)dy=(2x-8y)dx
limit as n approaches 6 of (-1)^n7n	\lim\:_{n\to\:6}((-1)^{n}7n)
limit as x approaches 3 of-x^2+9x-8	\lim\:_{x\to\:3}(-x^{2}+9x-8)
derivative of f(x)=dcos(t)+t^2sin(t)	derivative\:f(x)=d\cos(t)+t^{2}\sin(t)
d/(dt)(1+4sqrt(t))	\frac{d}{dt}(1+4\sqrt{t})
y^{''}-2y^'+5y=0,y(pi/2)=0,y^'(pi/2)=2	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=0,y(\frac{π}{2})=0,y^{\prime\:}(\frac{π}{2})=2
limit as x approaches 0 of (ln(x))-1/x	\lim\:_{x\to\:0}((\ln(x))-\frac{1}{x})
limit as x approaches-2 of-(x^2-x+1)	\lim\:_{x\to\:-2}(-(x^{2}-x+1))
integral from 1 to 2 of x^{10}	\int\:_{1}^{2}x^{10}dx
derivative of y= 5/(x^2)	derivative\:y=\frac{5}{x^{2}}
derivative of ln(e^{7x-2})	derivative\:\ln(e^{7x-2})
y^{''}+4y^'+10y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+4y^{\prime\:}+10y=0,y(0)=1,y^{\prime\:}(0)=0
derivative of 1/(2+cos(x))	\frac{d}{dx}(\frac{1}{2+\cos(x)})
integral of 4e^xcos(2x)	\int\:4e^{x}\cos(2x)dx
tangent of f(x)=(1+3x)(5-2x),\at x=2	tangent\:f(x)=(1+3x)(5-2x),\at\:x=2
inverse oflaplace s/((s+1)(s^2+4))	inverselaplace\:\frac{s}{(s+1)(s^{2}+4)}
(d^2)/(dx^2)(1/(x^{10)})	\frac{d^{2}}{dx^{2}}(\frac{1}{x^{10}})
integral of-tan(t)	\int\:-\tan(t)dt
inverse oflaplace 3/((s+1)^2+1)	inverselaplace\:\frac{3}{(s+1)^{2}+1}
(\partial)/(\partial x)(y/x-1)	\frac{\partial\:}{\partial\:x}(\frac{y}{x}-1)
derivative of f(x)=cos((x^2-25)/(x-5))	derivative\:f(x)=\cos(\frac{x^{2}-25}{x-5})
limit as x approaches 0 of (2x+x^2)/x	\lim\:_{x\to\:0}(\frac{2x+x^{2}}{x})
integral of 4x^3nxx	\int\:4x^{3}nxxdx
(dy)/(dx)=(y^2-x^2)/(2xy)	\frac{dy}{dx}=\frac{y^{2}-x^{2}}{2xy}
inverse oflaplace (s^4+1)/(s^3-s)	inverselaplace\:\frac{s^{4}+1}{s^{3}-s}
integral of sin(8x)cos(4x)	\int\:\sin(8x)\cos(4x)dx
tangent of f(x)=(4x)/(x-3),\at x=5	tangent\:f(x)=\frac{4x}{x-3},\at\:x=5
5y^{''}+y^'=-6x	5y^{\prime\:\prime\:}+y^{\prime\:}=-6x
(\partial)/(\partial x)(y-3x)	\frac{\partial\:}{\partial\:x}(y-3x)
limit as x approaches 0 of x/(sin(pix))	\lim\:_{x\to\:0}(\frac{x}{\sin(πx)})
limit as x approaches-infinity of x^5	\lim\:_{x\to\:-\infty\:}(x^{5})
limit as x approaches 1 of 3x^2+2x+1	\lim\:_{x\to\:1}(3x^{2}+2x+1)
derivative of xcos(1/x)	\frac{d}{dx}(x\cos(\frac{1}{x}))
limit as x approaches-1 of (x+2x^3)^4	\lim\:_{x\to\:-1}((x+2x^{3})^{4})
integral of (x^5)/(sqrt(1-2x^2))	\int\:\frac{x^{5}}{\sqrt{1-2x^{2}}}dx
integral of sqrt(1+4r^2)r	\int\:\sqrt{1+4r^{2}}rdr
integral of 3/(sqrt(e^x))	\int\:\frac{3}{\sqrt{e^{x}}}dx
derivative of f(x)=2^{x^2}	derivative\:f(x)=2^{x^{2}}
integral from 0 to 4 of pi((y^2)/2)^2	\int\:_{0}^{4}π(\frac{y^{2}}{2})^{2}dy
integral from 3 to 5 of 1/(4+(x-3)^2)	\int\:_{3}^{5}\frac{1}{4+(x-3)^{2}}dx
y^'+3y=e^xy^2	y^{\prime\:}+3y=e^{x}y^{2}
limit as x approaches 4+of (x+5)/(x-4)	\lim\:_{x\to\:4+}(\frac{x+5}{x-4})
9y^{''}+y=0	9y^{\prime\:\prime\:}+y=0
y^{''}+4y=t^2+3e^t	y^{\prime\:\prime\:}+4y=t^{2}+3e^{t}
integral from 0 to pi of cos^6(x)	\int\:_{0}^{π}\cos^{6}(x)dx
y^'=0.285(1-y)	y^{\prime\:}=0.285(1-y)
100y^{''}=0	100y^{\prime\:\prime\:}=0
limit as x approaches 3 of 5x^2	\lim\:_{x\to\:3}(5x^{2})
derivative of x^{-2/3}(x+5)	\frac{d}{dx}(x^{-\frac{2}{3}}(x+5))
derivative of (6x+8x^2/((3+8x)^2))	\frac{d}{dx}(\frac{6x+8x^{2}}{(3+8x)^{2}})
derivative of f(x)=sqrt(2x^2+1)	derivative\:f(x)=\sqrt{2x^{2}+1}
integral of (8e^{2x})/(e^{2x)+3e^x+2}	\int\:\frac{8e^{2x}}{e^{2x}+3e^{x}+2}dx
derivative of 6cos(x)csc(x^2)	derivative\:6\cos(x)\csc(x^{2})
laplacetransform cos(3t+5)	laplacetransform\:\cos(3t+5)
limit as x approaches-2+of 2x+sqrt(2+x)	\lim\:_{x\to\:-2+}(2x+\sqrt{2+x})
tangent of x^2+x+4	tangent\:x^{2}+x+4
y^{''}-3y^'+7y=4e^{3t}	y^{\prime\:\prime\:}-3y^{\prime\:}+7y=4e^{3t}
limit as x approaches 1 of \sqrt[3]{x-1}	\lim\:_{x\to\:1}(\sqrt[3]{x-1})
limit as x approaches 0+of (ln(x))/(1/x)	\lim\:_{x\to\:0+}(\frac{\ln(x)}{\frac{1}{x}})
tangent of f(x)=x^3-3x-5,\at x=1	tangent\:f(x)=x^{3}-3x-5,\at\:x=1
(\partial)/(\partial x)(ln(x+6y+8z))	\frac{\partial\:}{\partial\:x}(\ln(x+6y+8z))
(dy)/(dx)=-2/(x^3)+2e^{2x-2}	\frac{dy}{dx}=-\frac{2}{x^{3}}+2e^{2x-2}
tangent of f(x)=2x^2+5x^2-2,\at x=2	tangent\:f(x)=2x^{2}+5x^{2}-2,\at\:x=2
slope of y=x^2+6	slope\:y=x^{2}+6
integral from-1 to 1 of \|x^3-x\|	\int\:_{-1}^{1}\left\|x^{3}-x\right\|dx
integral of (sin^2(x))/4	\int\:\frac{\sin^{2}(x)}{4}dx
integral from 0 to infinity of sin^2(x)	\int\:_{0}^{\infty\:}\sin^{2}(x)dx
limit as x approaches 5 of (3x^2-x-2)0	\lim\:_{x\to\:5}((3x^{2}-x-2)0)
derivative of f(x)=arccsc(2x^4-5)	derivative\:f(x)=\arccsc(2x^{4}-5)
integral from 1 to 2 of ((x-4)^2)/(x^5)	\int\:_{1}^{2}\frac{(x-4)^{2}}{x^{5}}dx
slope of (11/8 ,-1/2),(1/4 , 1/4)	slope\:(\frac{11}{8},-\frac{1}{2}),(\frac{1}{4},\frac{1}{4})
limit as x approaches 0 of (sin(3))/(2x)	\lim\:_{x\to\:0}(\frac{\sin(3)}{2x})
normal of y=3x^2,(-4,48)	normal\:y=3x^{2},(-4,48)

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