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Popular Calculus Problems

y^{''}+4y=cos(2x)+sin(2x)	y^{\prime\:\prime\:}+4y=\cos(2x)+\sin(2x)
sum from n=0 to infinity of x^{3n}	\sum\:_{n=0}^{\infty\:}x^{3n}
integral of 24e^{20t}	\int\:24e^{20t}dt
integral of 3x^2ln(\sqrt[3]{x-1})	\int\:3x^{2}\ln(\sqrt[3]{x-1})dx
limit as x approaches-3-of 2/(x^2-9)	\lim\:_{x\to\:-3-}(\frac{2}{x^{2}-9})
derivative of y=x^5+cos^5(x)	derivative\:y=x^{5}+\cos^{5}(x)
limit as x approaches 90+of tan(x)	\lim\:_{x\to\:90+}(\tan(x))
(dy)/(dx)+(5/x)y=-x+5	\frac{dy}{dx}+(\frac{5}{x})y=-x+5
partialfraction x/((2x+3))	partialfraction\:\frac{x}{(2x+3)}
derivative of f(x)3x^4(x^2-2x)	derivative\:f(x)3x^{4}(x^{2}-2x)
(\partial)/(\partial x)(2/3 (x^2+1)^{3/2})	\frac{\partial\:}{\partial\:x}(\frac{2}{3}(x^{2}+1)^{\frac{3}{2}})
y^{''}-0.02y=0,y^'(0)=2,y(0)=0	y^{\prime\:\prime\:}-0.02y=0,y^{\prime\:}(0)=2,y(0)=0
limit as x approaches 2 of x^3f(2)	\lim\:_{x\to\:2}(x^{3}f(2))
integral of 2/(xsqrt(x^2-9))	\int\:\frac{2}{x\sqrt{x^{2}-9}}dx
derivative of y=3x^{-2}-5x^{-3}+3x^{-1}	derivative\:y=3x^{-2}-5x^{-3}+3x^{-1}
(\partial)/(\partial y)(xtan(y+z))	\frac{\partial\:}{\partial\:y}(x\tan(y+z))
integral of (x^4+1)/(x+1)	\int\:\frac{x^{4}+1}{x+1}dx
integral of 1/((x-1)(x-4))	\int\:\frac{1}{(x-1)(x-4)}dx
tangent of f(x)= 1/(3+2x),\at x=2	tangent\:f(x)=\frac{1}{3+2x},\at\:x=2
integral of (x^2)/(1+x^4)	\int\:\frac{x^{2}}{1+x^{4}}dx
integral of 1/(sqrt(1-9x^2))	\int\:\frac{1}{\sqrt{1-9x^{2}}}dx
(dy)/(dx)=e^{3x+2y}	\frac{dy}{dx}=e^{3x+2y}
limit as n approaches infinity of n/6 sin(6/n)	\lim\:_{n\to\:\infty\:}(\frac{n}{6}\sin(\frac{6}{n}))
integral of e^{tan(5x)}sec^2(5x)	\int\:e^{\tan(5x)}\sec^{2}(5x)dx
(dy)/(dx)=-((x+y)^2)/(2xy+x^2-1)	\frac{dy}{dx}=-\frac{(x+y)^{2}}{2xy+x^{2}-1}
derivative of ((1-2x)/(1+2x))	\frac{d}{dx}(\frac{(1-2x)}{1+2x})
(\partial)/(\partial x)(8x^5y^6+6x^4y^8)	\frac{\partial\:}{\partial\:x}(8x^{5}y^{6}+6x^{4}y^{8})
derivative of 6x^{-4}	derivative\:6x^{-4}
(\partial)/(\partial x)(5y^{1/4}x^{1/2})	\frac{\partial\:}{\partial\:x}(5y^{\frac{1}{4}}x^{\frac{1}{2}})
integral of x^3sqrt(4+x^4)	\int\:x^{3}\sqrt{4+x^{4}}dx
integral of (3\sqrt[4]{x^3}-8x^5+6e^x-2)	\int\:(3\sqrt[4]{x^{3}}-8x^{5}+6e^{x}-2)dx
(dy)/(dx)=y(3-y)	\frac{dy}{dx}=y(3-y)
limit as x approaches+(-1)-of x^2+1	\lim\:_{x\to\:+(-1)-}(x^{2}+1)
derivative of+2x	\frac{d}{dx}(+2x)
tangent of f(x)=6sqrt(x),(9,18)	tangent\:f(x)=6\sqrt{x},(9,18)
f(x)=tan^3(x)	f(x)=\tan^{3}(x)
derivative of ((x-3/(sqrt(2x+1)))^4)	\frac{d}{dx}((\frac{x-3}{\sqrt{2x+1}})^{4})
integral from 12 to 13 of xsqrt(x^2-144)	\int\:_{12}^{13}x\sqrt{x^{2}-144}dx
(\partial)/(\partial x)(xy-ln(xy))	\frac{\partial\:}{\partial\:x}(xy-\ln(xy))
derivative of ((6x^2+4)/((3y^2-4)))	\frac{d}{dx}(\frac{(6x^{2}+4)}{(3y^{2}-4)})
integral from-3 to 0 of 1+sqrt(9-x^2)	\int\:_{-3}^{0}1+\sqrt{9-x^{2}}dx
inverse oflaplace (200)/((s+10)(s+100))	inverselaplace\:\frac{200}{(s+10)(s+100)}
x^{''}-x=0	x^{\prime\:\prime\:}-x=0
derivative of x^3-2x^2+x-20	\frac{d}{dx}(x^{3}-2x^{2}+x-20)
integral from 0 to 1 of xsin(npix)	\int\:_{0}^{1}x\sin(nπx)dx
(\partial)/(\partial y)(y^4)	\frac{\partial\:}{\partial\:y}(y^{4})
derivative of sqrt(sec(x)*x^5)	\frac{d}{dx}(\sqrt{\sec(x)}\cdot\:x^{5})
(\partial)/(\partial x)(x+2y+z)	\frac{\partial\:}{\partial\:x}(x+2y+z)
integral of (12x+30)/(x^2+2x-8)	\int\:\frac{12x+30}{x^{2}+2x-8}dx
limit as x approaches 1 of e^{x^2+7x-8}	\lim\:_{x\to\:1}(e^{x^{2}+7x-8})
limit as x approaches 2 of 2/(x+2)	\lim\:_{x\to\:2}(\frac{2}{x+2})
derivative of (2x/5)	\frac{d}{dx}(\frac{2x}{5})
y^'=((x^2-y^2))/(xy),y(2)=5	y^{\prime\:}=\frac{(x^{2}-y^{2})}{xy},y(2)=5
tangent of f(x)=4sec(x),\at (pi/6)	tangent\:f(x)=4\sec(x),\at\:(\frac{π}{6})
integral of (x^3)/(x^2+10x+25)	\int\:\frac{x^{3}}{x^{2}+10x+25}dx
(\partial)/(\partial x)(log_{10}(x+y))	\frac{\partial\:}{\partial\:x}(\log_{10}(x+y))
integral of tsin(9t)	\int\:t\sin(9t)dt
slope of (2.3)(4.4)	slope\:(2.3)(4.4)
(\partial)/(\partial y)(4ysqrt(x))	\frac{\partial\:}{\partial\:y}(4y\sqrt{x})
limit as x approaches 3 of 2/(x^2-9)	\lim\:_{x\to\:3}(\frac{2}{x^{2}-9})
area y=x,4x+y^2=12	area\:y=x,4x+y^{2}=12
inverse oflaplace {5/(s^2+49)}	inverselaplace\:\left\{\frac{5}{s^{2}+49}\right\}
derivative of (a+3y^2+b)^{1/2}	derivative\:(a+3y^{2}+b)^{\frac{1}{2}}
derivative of f(x)=(pi^2)/(x^2+4x)	derivative\:f(x)=\frac{π^{2}}{x^{2}+4x}
integral of-1/27 sin(3x)	\int\:-\frac{1}{27}\sin(3x)dx
integral of (3-5x)/(sqrt(9-5x^2))	\int\:\frac{3-5x}{\sqrt{9-5x^{2}}}dx
derivative of arccos(6/x)	\frac{d}{dx}(\arccos(\frac{6}{x}))
(\partial)/(\partial v)(e^{{u}(v)}+sin(v))	\frac{\partial\:}{\partial\:v}(e^{{u}(v)}+\sin(v))
integral from 1 to 2 of (-y^3+2y^2+5y-6)	\int\:_{1}^{2}(-y^{3}+2y^{2}+5y-6)dy
integral from-3 to 3 of \|2x-1\|	\int\:_{-3}^{3}\left\|2x-1\right\|dx
integral of 3x^2sqrt(x^3+1)	\int\:3x^{2}\sqrt{x^{3}+1}dx
integral from 0 to 1 of 4x^3e^{x^4}	\int\:_{0}^{1}4x^{3}e^{x^{4}}dx
xsqrt(1-y^2)dx+ysqrt(1+x^2)dy=0	x\sqrt{1-y^{2}}dx+y\sqrt{1+x^{2}}dy=0
integral from 0 to 1 of 1/(x^2-3)	\int\:_{0}^{1}\frac{1}{x^{2}-3}dx
integral of (9x^2+x+48)/((x+3)(x^2+9))	\int\:\frac{9x^{2}+x+48}{(x+3)(x^{2}+9)}dx
(\partial)/(\partial y)(xye^{sin(pixy)})	\frac{\partial\:}{\partial\:y}(xye^{\sin(πxy)})
area y=2,y=sec(x)	area\:y=2,y=\sec(x)
d/(dt)(sin^2(pit))	\frac{d}{dt}(\sin^{2}(πt))
d/(d{x)}(1/(sqrt({x)^2+{y)^2+{z}^2}})	\frac{d}{d{x}}(\frac{1}{\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}})
(\partial)/(\partial x)(xe^{x^2y})	\frac{\partial\:}{\partial\:x}(xe^{x^{2}y})
derivative of (-40)/(x^7)	derivative\:\frac{-40}{x^{7}}
limit as x approaches 1+of x^{1/((1-x))}	\lim\:_{x\to\:1+}(x^{\frac{1}{(1-x)}})
derivative of-1/(x+1)	\frac{d}{dx}(-\frac{1}{x+1})
d/(ds)(sL({y}(s)))	\frac{d}{ds}(sL({y}(s)))
integral of (1+arctan(x))/(1+x^2)	\int\:\frac{1+\arctan(x)}{1+x^{2}}dx
(\partial)/(\partial y)(1/2 (x-y)^2)	\frac{\partial\:}{\partial\:y}(\frac{1}{2}(x-y)^{2})
limit as x approaches 2 of x^2-4x+2	\lim\:_{x\to\:2}(x^{2}-4x+2)
inverse oflaplace 1/(2s^2+s)	inverselaplace\:\frac{1}{2s^{2}+s}
integral of 1/(x^1)	\int\:\frac{1}{x^{1}}dx
integral of (sin(1+sqrt(x)))/(sqrt(x))	\int\:\frac{\sin(1+\sqrt{x})}{\sqrt{x}}dx
integral from x to 5 of sin(t^3)	\int\:_{x}^{5}\sin(t^{3})dt
integral of tan^4(9x)	\int\:\tan^{4}(9x)dx
derivative of f(x)= 2/x-1/(x^2)	derivative\:f(x)=\frac{2}{x}-\frac{1}{x^{2}}
integral of (\sqrt[3]{x}+1/(sqrt(x)))	\int\:(\sqrt[3]{x}+\frac{1}{\sqrt{x}})dx
tangent of f(x)= x/(1+x^2),(2,0.4)	tangent\:f(x)=\frac{x}{1+x^{2}},(2,0.4)
derivative of (1-sin(x)^{-1/2})	\frac{d}{dx}((1-\sin(x))^{-\frac{1}{2}})
integral of (361)/(x^3-19x^2)	\int\:\frac{361}{x^{3}-19x^{2}}dx
derivative of 1/20 e^x+x^6-x^e+e	\frac{d}{dx}(\frac{1}{20}e^{x}+x^{6}-x^{e}+e)
(\partial)/(\partial x)(sin^9(x))	\frac{\partial\:}{\partial\:x}(\sin^{9}(x))
(\partial)/(\partial y)(y*cos(y-2x))	\frac{\partial\:}{\partial\:y}(y\cdot\:\cos(y-2x))

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