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Popular Calculus Problems

derivative of ln((x^2+4x+5^3))	\frac{d}{dx}(\ln((x^{2}+4x+5)^{3}))
integral of e-e^x	\int\:e-e^{x}dx
laplacetransform 1/2 sin(4t)	laplacetransform\:\frac{1}{2}\sin(4t)
xy^'+y=-3x	xy^{\prime\:}+y=-3x
integral of (x-2)/x	\int\:\frac{x-2}{x}dx
inverse oflaplace s/((s-2)^2)	inverselaplace\:\frac{s}{(s-2)^{2}}
integral of (e^{-bx})/(1-e^{-bx)}	\int\:\frac{e^{-bx}}{1-e^{-bx}}dx
derivative of f(x)=y	derivative\:f(x)=y
inverse oflaplace (-s)/(s^2+25s+30)+1/s	inverselaplace\:\frac{-s}{s^{2}+25s+30}+\frac{1}{s}
integral of e^{2x}(1-3x)	\int\:e^{2x}(1-3x)dx
limit as x approaches 4 of e^x	\lim\:_{x\to\:4}(e^{x})
d/(da)(sin(a)-cos(a))	\frac{d}{da}(\sin(a)-\cos(a))
derivative of-(sin(x))/(cos(x))	derivative\:-\frac{\sin(x)}{\cos(x)}
x^'-10x=0	x^{\prime\:}-10x=0
y^{''}-12y^'+36y=30x+2	y^{\prime\:\prime\:}-12y^{\prime\:}+36y=30x+2
integral of 12y	\int\:12ydy
derivative of f(x)= 1/(4x^2+5x)	derivative\:f(x)=\frac{1}{4x^{2}+5x}
derivative of (925+20x-0.079x^2)/(484)	derivative\:\frac{925+20x-0.079x^{2}}{484}
derivative of (csc^2(x-cot^3(x))/(tan(x^2+2x)))	\frac{d}{dx}(\frac{\csc^{2}(x)-\cot^{3}(x)}{\tan(x^{2}+2x)})
integral from 9 to 24 of (-x+12)	\int\:_{9}^{24}(-x+12)dx
taylor ln(s)	taylor\:\ln(s)
y^'=(3y^2+4x)/(2xy)	y^{\prime\:}=\frac{3y^{2}+4x}{2xy}
integral of (x^2)/(sqrt(-4x^2-12x-5))	\int\:\frac{x^{2}}{\sqrt{-4x^{2}-12x-5}}dx
limit as x approaches 8 of ((\sqrt[3]{x}-2))/((x-8))	\lim\:_{x\to\:8}(\frac{(\sqrt[3]{x}-2)}{(x-8)})
f^'(x)=((5x^2-9x+8))/(7x+6)	f^{\prime\:}(x)=\frac{(5x^{2}-9x+8)}{7x+6}
integral of x^5cos(2x)	\int\:x^{5}\cos(2x)dx
tangent of y=(1+4x)^{3/2},\at x=2	tangent\:y=(1+4x)^{\frac{3}{2}},\at\:x=2
(x+2y)dx+(2x-y)dy=0	(x+2y)dx+(2x-y)dy=0
y^{''}-3y^'+2y=0	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=0
sqrt(x)+sqrt(y)y^'=0	\sqrt{x}+\sqrt{y}y^{\prime\:}=0
integral of 1/(p^2+1)	\int\:\frac{1}{p^{2}+1}dp
derivative of xe^y+y^2e^x-1/3 x+4	\frac{d}{dx}(xe^{y}+y^{2}e^{x}-\frac{1}{3}x+4)
integral of xe^{3x^2}	\int\:xe^{3x^{2}}dx
derivative of e^{ix}	\frac{d}{dx}(e^{ix})
integral of (2cos(ln(x)))/x	\int\:\frac{2\cos(\ln(x))}{x}dx
(\partial)/(\partial y)(e^{x^y})	\frac{\partial\:}{\partial\:y}(e^{x^{y}})
(\partial)/(\partial x)(sqrt((a+x)^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{(a+x)^{2}+y^{2}})
integral of 5/(cos^2(x))	\int\:\frac{5}{\cos^{2}(x)}dx
(d^2y)/(dx^2)+14(dy)/(dx)+98y=0	\frac{d^{2}y}{dx^{2}}+14\frac{dy}{dx}+98y=0
(3xy^2+1y)dx+(3x^2y+1x)dy=0	(3xy^{2}+1y)dx+(3x^{2}y+1x)dy=0
(dy)/(dx)=(4x-1)(y+5)	\frac{dy}{dx}=(4x-1)(y+5)
(xe^{-x^2})^'	(xe^{-x^{2}})^{\prime\:}
integral of ((x+3))/((x^2+6x)^{1/3)}	\int\:\frac{(x+3)}{(x^{2}+6x)^{\frac{1}{3}}}dx
(dy)/(dx)=(3x^4+y^3)/(3xy^2)	\frac{dy}{dx}=\frac{3x^{4}+y^{3}}{3xy^{2}}
(dy)/(dt)= 1/(y-2)	\frac{dy}{dt}=\frac{1}{y-2}
sum from n=0 to infinity of (-5/6)^n	\sum\:_{n=0}^{\infty\:}(-\frac{5}{6})^{n}
integral of cos^2(θ)+sin^2(θ)	\int\:\cos^{2}(θ)+\sin^{2}(θ)dθ
limit as x approaches+0 of x^4cos(pi/x)	\lim\:_{x\to\:+0}(x^{4}\cos(\frac{π}{x}))
derivative of f(x)=(e^x)/(2+4x)	derivative\:f(x)=\frac{e^{x}}{2+4x}
f(x)=-2sin(2x)	f(x)=-2\sin(2x)
integral of 6sec^2(x)	\int\:6\sec^{2}(x)dx
integral of x^3(ln(x))^2	\int\:x^{3}(\ln(x))^{2}dx
inverse oflaplace s/((s^2+4))	inverselaplace\:\frac{s}{(s^{2}+4)}
limit as x approaches 1 of (x^2-2)^3	\lim\:_{x\to\:1}((x^{2}-2)^{3})
derivative of f(x)=6sec(x)tan(x)	derivative\:f(x)=6\sec(x)\tan(x)
integral from 0 to 7 of 1/(sqrt(49+x^2))	\int\:_{0}^{7}\frac{1}{\sqrt{49+x^{2}}}dx
integral of 1/(sqrt(4-y^2))	\int\:\frac{1}{\sqrt{4-y^{2}}}dy
y^'=sin(y)	y^{\prime\:}=\sin(y)
integral of (8t^3-3t^2+32t)/(t^2+4)	\int\:\frac{8t^{3}-3t^{2}+32t}{t^{2}+4}dt
(\partial)/(\partial y)(x^{7y})	\frac{\partial\:}{\partial\:y}(x^{7y})
derivative of ln(-2x)	\frac{d}{dx}(\ln(-2x))
integral of-(8x^3)/((5-2x^4)^4)	\int\:-\frac{8x^{3}}{(5-2x^{4})^{4}}dx
10y^{''}-y^'-3y=0,y(0)=1,y^'(0)=0	10y^{\prime\:\prime\:}-y^{\prime\:}-3y=0,y(0)=1,y^{\prime\:}(0)=0
derivative of (1-0.6x/x)	\frac{d}{dx}(\frac{1-0.6x}{x})
(\partial)/(\partial x)(x/(1+xy))	\frac{\partial\:}{\partial\:x}(\frac{x}{1+xy})
derivative of 3x+6	\frac{d}{dx}(3x+6)
y^'-3y=6	y^{\prime\:}-3y=6
derivative of f(x)=cos(sin(x^2))	derivative\:f(x)=\cos(\sin(x^{2}))
integral of (x+1)^{-3}	\int\:(x+1)^{-3}dx
integral of (x^2)/(sqrt(x^3-2))	\int\:\frac{x^{2}}{\sqrt{x^{3}-2}}dx
derivative of cf(x)	derivative\:cf(x)
limit as x approaches 0-of 5+2/x	\lim\:_{x\to\:0-}(5+\frac{2}{x})
integral of 1/((sin(x)-cos(x)-1))	\int\:\frac{1}{(\sin(x)-\cos(x)-1)}dx
f(x)=ln(3)x^2	f(x)=\ln(3)x^{2}
derivative of 9e^{9e^x+x}	derivative\:9e^{9e^{x}+x}
derivative of 6x+6	\frac{d}{dx}(6x+6)
y^{''}+9y=sec(3x)	y^{\prime\:\prime\:}+9y=\sec(3x)
integral of (6z)/((5-3z^2)^2)	\int\:\frac{6z}{(5-3z^{2})^{2}}dz
integral of 7xe^{x^2}	\int\:7xe^{x^{2}}dx
limit as x approaches pi/4 of-cos(x)	\lim\:_{x\to\:\frac{π}{4}}(-\cos(x))
y^{''}=-2y	y^{\prime\:\prime\:}=-2y
derivative of y/(x+y^2)	\frac{d}{dx}(\frac{y}{x+y^{2}})
integral of (x^2-2x-1)/(2x^3+3x^2-2x)	\int\:\frac{x^{2}-2x-1}{2x^{3}+3x^{2}-2x}dx
integral of (x^2)/(e^{5x)}	\int\:\frac{x^{2}}{e^{5x}}dx
derivative of 3x^2cos(xcot(x))	\frac{d}{dx}(3x^{2}\cos(x)\cot(x))
limit as x approaches-infinity of (5x^2-sin(3x))/(x^2+10)	\lim\:_{x\to\:-\infty\:}(\frac{5x^{2}-\sin(3x)}{x^{2}+10})
derivative of tan(5-sin(2x))	\frac{d}{dx}(\tan(5-\sin(2x)))
y^'=(cos^2(x))(cos^2(6y))	y^{\prime\:}=(\cos^{2}(x))(\cos^{2}(6y))
(dy)/(dx)=sqrt(7y)e^{x+6}	\frac{dy}{dx}=\sqrt{7y}e^{x+6}
derivative of f(x)=cos(a^4+x^4)	derivative\:f(x)=\cos(a^{4}+x^{4})
integral of (sin(t))^2	\int\:(\sin(t))^{2}dt
limit as x approaches 0 of (3^x-1)/x	\lim\:_{x\to\:0}(\frac{3^{x}-1}{x})
f(x)=(-4x^2+3x-7)/(2x^2-10x-3)	f(x)=\frac{-4x^{2}+3x-7}{2x^{2}-10x-3}
integral of-e^{-kt}kM	\int\:-e^{-kt}kMdt
(\partial)/(\partial x)(arctan(xy)-z)	\frac{\partial\:}{\partial\:x}(\arctan(xy)-z)
limit as x approaches 0 of-3(-6)+3(-5)	\lim\:_{x\to\:0}(-3(-6)+3(-5))
area y=x^3-4x,-2<= x<= 2	area\:y=x^{3}-4x,-2\le\:x\le\:2
(\partial)/(\partial x)(y^x)	\frac{\partial\:}{\partial\:x}(y^{x})
integral of cos^2(x^2)	\int\:\cos^{2}(x^{2})dx
integral of 1/(sqrt(25+x^2))	\int\:\frac{1}{\sqrt{25+x^{2}}}dx

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