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Popular Calculus Problems

x(dy)/(dx)+2y=-2sin(x)	x\frac{dy}{dx}+2y=-2\sin(x)
integral from 0 to 4 of (5x-x^2)-x	\int\:_{0}^{4}(5x-x^{2})-xdx
f(x)=2x^2e^x	f(x)=2x^{2}e^{x}
(d^2)/(dx^2)(1/(1+x))	\frac{d^{2}}{dx^{2}}(\frac{1}{1+x})
limit as h approaches 0 of 1/(sqrt(3h))	\lim\:_{h\to\:0}(\frac{1}{\sqrt{3h}})
derivative of (cos(x)/(e^{2x)}-2)	\frac{d}{dx}(\frac{\cos(x)}{e^{2x}}-2)
y^'+1/x y=2	y^{\prime\:}+\frac{1}{x}y=2
limit as n approaches infinity of (4/5)^n	\lim\:_{n\to\:\infty\:}((\frac{4}{5})^{n})
integral from 0 to 6r of sqrt(36r^2-y^2)	\int\:_{0}^{6r}\sqrt{36r^{2}-y^{2}}dy
limit as x approaches infinity of ln(6x)	\lim\:_{x\to\:\infty\:}(\ln(6x))
y^3-(2x+6)+3xy^2y^'=0	y^{3}-(2x+6)+3xy^{2}y^{\prime\:}=0
derivative of g(x)=sqrt(13x)	derivative\:g(x)=\sqrt{13x}
limit as x approaches-1+of 2-x	\lim\:_{x\to\:-1+}(2-x)
limit as x approaches 6+of 2/(x-6)	\lim\:_{x\to\:6+}(\frac{2}{x-6})
integral of (x^2)/((x^2-4)^{3/2)}	\int\:\frac{x^{2}}{(x^{2}-4)^{\frac{3}{2}}}dx
(dy)/(dx)=(1+y^2)/(1+x^2)	\frac{dy}{dx}=\frac{1+y^{2}}{1+x^{2}}
derivative of 5x^{1/2}	derivative\:5x^{\frac{1}{2}}
2ty^'-4y=4t^4e^{t^2},y(1)=0	2ty^{\prime\:}-4y=4t^{4}e^{t^{2}},y(1)=0
derivative of-6/((1+x^4))	\frac{d}{dx}(-\frac{6}{(1+x)^{4}})
integral of 1/(sqrt(1+5x^2))	\int\:\frac{1}{\sqrt{1+5x^{2}}}dx
integral of 4sin^3(xco)s^2x	\int\:4\sin^{3}(xco)s^{2}xdx
tangent of y=sqrt(x+225),(0,15)	tangent\:y=\sqrt{x+225},(0,15)
integral of 2x^2-2	\int\:2x^{2}-2dx
derivative of (1-x^2/x)	\frac{d}{dx}(\frac{1-x^{2}}{x})
derivative of x^2-x^3+3	\frac{d}{dx}(x^{2}-x^{3}+3)
integral of (e^{ln^2(x)})/x ln(x)	\int\:\frac{e^{\ln^{2}(x)}}{x}\ln(x)dx
derivative of y= 8/(sqrt(x-7))	derivative\:y=\frac{8}{\sqrt{x-7}}
derivative of 2x+cos(x)	\frac{d}{dx}(2x+\cos(x))
integral of x^{27}e^{-x^{28}}	\int\:x^{27}e^{-x^{28}}dx
integral from-2 to 5 of \|x-2\|	\int\:_{-2}^{5}\left\|x-2\right\|dx
derivative of (1+(10)/x)^8	derivative\:(1+\frac{10}{x})^{8}
integral of x/((x+2)^2)	\int\:\frac{x}{(x+2)^{2}}dx
area 3x,x^2	area\:3x,x^{2}
derivative of-4x^{4/3}-2x^{-3/4}+3	\frac{d}{dx}(-4x^{\frac{4}{3}}-2x^{-\frac{3}{4}}+3)
derivative of y=sec(x)	derivative\:y=\sec(x)
integral of-e^{1-x}	\int\:-e^{1-x}dx
integral of (2y)/x	\int\:\frac{2y}{x}dx
(\partial)/(\partial r)(1/3 pir^2h)	\frac{\partial\:}{\partial\:r}(\frac{1}{3}πr^{2}h)
derivative of f(x)=((5x-2))/((x^2+1))	derivative\:f(x)=\frac{(5x-2)}{(x^{2}+1)}
integral from 0 to pi/8 of sec^2(2x)	\int\:_{0}^{\frac{π}{8}}\sec^{2}(2x)dx
integral from 0 to pi/6 of 1	\int\:_{0}^{\frac{π}{6}}1
limit as x approaches 0-of x^{sin(x)}	\lim\:_{x\to\:0-}(x^{\sin(x)})
derivative of y=(1+sqrt(x))^3	derivative\:y=(1+\sqrt{x})^{3}
d/(dt)(sec^2(t))	\frac{d}{dt}(\sec^{2}(t))
derivative of (x^2-100)/(x+10)	derivative\:\frac{x^{2}-100}{x+10}
derivative of (6a+1)^2	derivative\:(6a+1)^{2}
derivative of 10(3x+1(1-5x))	\frac{d}{dx}(10(3x+1)(1-5x))
(\partial)/(\partial x)((3x)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{3x}{x^{2}+y^{2}})
derivative of 4sec(x-7x)	\frac{d}{dx}(4\sec(x)-7x)
inverse oflaplace 2/((s^2+1))	inverselaplace\:\frac{2}{(s^{2}+1)}
integral of 6csc(x)	\int\:6\csc(x)dx
integral of cos(x)*sin^4(x)	\int\:\cos(x)\cdot\:\sin^{4}(x)dx
integral of ((x-1))/(x^2-x+1)	\int\:\frac{(x-1)}{x^{2}-x+1}dx
limit as x approaches-infinity of e^x-1	\lim\:_{x\to\:-\infty\:}(e^{x}-1)
limit as x approaches pi/4 of (sec^2(x)-2tan(x))/(1+cos(4x))	\lim\:_{x\to\:\frac{π}{4}}(\frac{\sec^{2}(x)-2\tan(x)}{1+\cos(4x)})
y^{''}-(6/x)y^'-(9/(x^2))y=0	y^{\prime\:\prime\:}-(\frac{6}{x})y^{\prime\:}-(\frac{9}{x^{2}})y=0
limit as x approaches-2+of (-2)/(x^2-4)	\lim\:_{x\to\:-2+}(\frac{-2}{x^{2}-4})
limit as x approaches+0 of 1/(sqrt(x))	\lim\:_{x\to\:+0}(\frac{1}{\sqrt{x}})
x^{''}+kx^'+x=0	x^{\prime\:\prime\:}+kx^{\prime\:}+x=0
derivative of (3x^2/4)	\frac{d}{dx}(\frac{3x^{2}}{4})
limit as x approaches 0+of cot(4x)	\lim\:_{x\to\:0+}(\cot(4x))
sum from n=1 to infinity of 1/(n^2+n+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+n+1}
derivative of 10(2e^{x^2}x^2+e^{x^2})	derivative\:10(2e^{x^{2}}x^{2}+e^{x^{2}})
sum from n=1 to infinity of (5n)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{5n}{n!}
derivative of (x/5-5/x ^5)	\frac{d}{dx}((\frac{x}{5}-\frac{5}{x})^{5})
integral from 0 to 2 of (2x-3)(4x^2+1)	\int\:_{0}^{2}(2x-3)(4x^{2}+1)dx
tangent of f(x)=4x^2+4x-2,\at x=-1	tangent\:f(x)=4x^{2}+4x-2,\at\:x=-1
derivative of (x^3+5e^x)	\frac{d}{dx}((x^{3}+5)e^{x})
integral of cos(4x)sqrt(2-sin(4x))	\int\:\cos(4x)\sqrt{2-\sin(4x)}dx
integral of 1/(sqrt((9-x^2)))	\int\:\frac{1}{\sqrt{(9-x^{2})}}dx
derivative of sqrt(4(x+4^3))	\frac{d}{dx}(\sqrt{4(x+4)^{3}})
tangent of f(x)=x^2-3x-2,\at x=2	tangent\:f(x)=x^{2}-3x-2,\at\:x=2
derivative of-b/(x^2)	\frac{d}{dx}(-\frac{b}{x^{2}})
(dy)/(dx)=(cos(7x))/(e^{7y)},y(0)=0	\frac{dy}{dx}=\frac{\cos(7x)}{e^{7y}},y(0)=0
limit as x approaches 1+of x^2-2	\lim\:_{x\to\:1+}(x^{2}-2)
y^{''}-6y+13y=0	y^{\prime\:\prime\:}-6y+13y=0
sum from n=1 to infinity of 2n-1	\sum\:_{n=1}^{\infty\:}2n-1
integral of (2x^3-4x-8)/((x^2-x)(x^2+4))	\int\:\frac{2x^{3}-4x-8}{(x^{2}-x)(x^{2}+4)}dx
derivative of 0.0588(80)^{1.125}	derivative\:0.0588(80)^{1.125}
(\partial)/(\partial x)((2x)/(2+y))	\frac{\partial\:}{\partial\:x}(\frac{2x}{2+y})
xy^'-2y=x^2-x-1	xy^{\prime\:}-2y=x^{2}-x-1
inverse oflaplace s/((s^3+1))	inverselaplace\:\frac{s}{(s^{3}+1)}
integral from a to b of 1/x	\int\:_{a}^{b}\frac{1}{x}dx
integral of-1/(x^4)	\int\:-\frac{1}{x^{4}}dx
derivative of e^{-1/(x^2})	\frac{d}{dx}(e^{-\frac{1}{x^{2}}})
integral of 3x^2-2x+1	\int\:3x^{2}-2x+1dx
dy+(2xy-4e^{-x^2})dx=0	dy+(2xy-4e^{-x^{2}})dx=0
slope of (4,1),(3,1)	slope\:(4,1),(3,1)
(x+y)^2dx+(2xy+x^2-6)dy=0	(x+y)^{2}dx+(2xy+x^{2}-6)dy=0
derivative of (xlog_{2}(x))^2	derivative\:(x\log_{2}(x))^{2}
integral of (log_{10}(x))/x	\int\:\frac{\log_{10}(x)}{x}dx
d/(dt)(e^{t^2-t})	\frac{d}{dt}(e^{t^{2}-t})
taylor arctan(x/2)	taylor\:\arctan(\frac{x}{2})
2y^{''}+50y=0	2y^{\prime\:\prime\:}+50y=0
integral of 1-(2x)/(x^2+1)	\int\:1-\frac{2x}{x^{2}+1}dx
integral of (x^3-2x^4+x^5)/2	\int\:\frac{x^{3}-2x^{4}+x^{5}}{2}dx
derivative of 3tan(x)	derivative\:3\tan(x)
tangent of f(x)=12sqrt(x),(9,36)	tangent\:f(x)=12\sqrt{x},(9,36)
sum from n=0 to infinity of 1/2*(-1)^n	\sum\:_{n=0}^{\infty\:}\frac{1}{2}\cdot\:(-1)^{n}
(\partial)/(\partial x)(-4xy-x^4-y^4)	\frac{\partial\:}{\partial\:x}(-4xy-x^{4}-y^{4})

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