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Popular Calculus Problems

inverse oflaplace 1/(s^2+3s)	inverselaplace\:\frac{1}{s^{2}+3s}
derivative of 2xe^x-e^{2x}	\frac{d}{dx}(2xe^{x}-e^{2x})
derivative of (2x^3+2(x^4-3x))	\frac{d}{dx}((2x^{3}+2)(x^{4}-3x))
tangent of f(x)= x/(1+x^2),(3,0.3)	tangent\:f(x)=\frac{x}{1+x^{2}},(3,0.3)
inverse oflaplace ((1))/((s-3)(s+1))	inverselaplace\:\frac{(1)}{(s-3)(s+1)}
integral of (sqrt(25x^2-1))/x	\int\:\frac{\sqrt{25x^{2}-1}}{x}dx
integral of 2(x+20)e^{x/(20)}	\int\:2(x+20)e^{\frac{x}{20}}dx
derivative of xcos(4x)	\frac{d}{dx}(x\cos(4x))
(x^2+1)y^'+9x(y-1)=0,y(0)=4	(x^{2}+1)y^{\prime\:}+9x(y-1)=0,y(0)=4
y+2t^2+y^'tln(t)=0	y+2t^{2}+y^{\prime\:}t\ln(t)=0
integral of (x+8)/(x^2+16)	\int\:\frac{x+8}{x^{2}+16}dx
(\partial)/(\partial y)(3x^2-2xy+2)	\frac{\partial\:}{\partial\:y}(3x^{2}-2xy+2)
(\partial)/(\partial x)(ln((3xy)/(5z)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{3xy}{5z}))
integral of (2x+1)sqrt(x-5)	\int\:(2x+1)\sqrt{x-5}dx
area \|4x-1\|,x^2-5	area\:\left\|4x-1\right\|,x^{2}-5
(dy)/(dx)=-((y^2)/(1+y^2)e^{(-x)})	\frac{dy}{dx}=-(\frac{y^{2}}{1+y^{2}}e^{(-x)})
limit as x approaches 0 of 1/8+x-(1/8)	\lim\:_{x\to\:0}(\frac{1}{8}+x-(\frac{1}{8}))
integral of (5x^2+3x-10)	\int\:(5x^{2}+3x-10)dx
integral of (18x^2)/(x^4-41x^2+400)	\int\:\frac{18x^{2}}{x^{4}-41x^{2}+400}dx
derivative of 4x-x^2-3	\frac{d}{dx}(4x-x^{2}-3)
limit as y approaches 15 of sqrt(y+3)	\lim\:_{y\to\:15}(\sqrt{y+3})
integral of (sin(2e^{-4x}))/(e^{4x)}	\int\:\frac{\sin(2e^{-4x})}{e^{4x}}dx
area f(x)=x^3-3x^2+3x,g(x)=x	area\:f(x)=x^{3}-3x^{2}+3x,g(x)=x
derivative of f(3)=2x^2+4x	derivative\:f(3)=2x^{2}+4x
integral of 1/(x^2sqrt(25x^2+64))	\int\:\frac{1}{x^{2}\sqrt{25x^{2}+64}}dx
(\partial)/(\partial y)(-3x^2y)	\frac{\partial\:}{\partial\:y}(-3x^{2}y)
area f(x)=x^2+4x,g(x)=x+10	area\:f(x)=x^{2}+4x,g(x)=x+10
inverse oflaplace 3/(s+5)	inverselaplace\:\frac{3}{s+5}
derivative of f(x)=ln(e^4)	derivative\:f(x)=\ln(e^{4})
integral of ((6x^3+6x))/(x^2+1)	\int\:\frac{(6x^{3}+6x)}{x^{2}+1}dx
(dy)/(dx)+3y=6	\frac{dy}{dx}+3y=6
integral of e^{-x}(x-1)	\int\:e^{-x}(x-1)dx
derivative of (x+2/(10-3x))	\frac{d}{dx}(\frac{x+2}{10-3x})
implicit (dy)/(dx),ax^3-3b^2xy+cy(x)^3=1	implicit\:\frac{dy}{dx},ax^{3}-3b^{2}xy+cy(x)^{3}=1
derivative of (-x^2-2x+1/((1+x^2)^2))	\frac{d}{dx}(\frac{-x^{2}-2x+1}{(1+x^{2})^{2}})
(x^2+1)y^'+8x(y-1)=0	(x^{2}+1)y^{\prime\:}+8x(y-1)=0
derivative of x^4-8x^3	derivative\:x^{4}-8x^{3}
(\partial)/(\partial x)(3/(3x+2y))	\frac{\partial\:}{\partial\:x}(\frac{3}{3x+2y})
(dy)/(dx)=(xy+x^2+y^2)/(x^2)	\frac{dy}{dx}=\frac{xy+x^{2}+y^{2}}{x^{2}}
derivative of 3x^3-4	\frac{d}{dx}(3x^{3}-4)
y^{''}+11y=0	y^{\prime\:\prime\:}+11y=0
tangent of x^2=2y	tangent\:x^{2}=2y
area y=9x,y= 3/7 x,y=52-x^2	area\:y=9x,y=\frac{3}{7}x,y=52-x^{2}
f(x)= x/(x^2+25)	f(x)=\frac{x}{x^{2}+25}
integral of 2x(x^2+3)^9	\int\:2x(x^{2}+3)^{9}dx
integral from 0 to 6 of x^3e^x	\int\:_{0}^{6}x^{3}e^{x}dx
sum from n=1 to infinity of 1/(n^2-1)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}-1}
integral from 0 to 1 of x^4e^{6x}	\int\:_{0}^{1}x^{4}e^{6x}dx
integral of-tsqrt(z)	\int\:-t\sqrt{z}dt
e^{2x}y^'-2e^{2x}y=3e^{4x}	e^{2x}y^{\prime\:}-2e^{2x}y=3e^{4x}
limit as x approaches 5-of (12)/(5-x)	\lim\:_{x\to\:5-}(\frac{12}{5-x})
derivative of e^x(8x^2-16x+16)	\frac{d}{dx}(e^{x}(8x^{2}-16x+16))
integral of x^{-6}	\int\:x^{-6}dx
derivative of y=-2/(x^3)	derivative\:y=-\frac{2}{x^{3}}
tangent of f(x)=x^2,\at (-3/8)	tangent\:f(x)=x^{2},\at\:(-\frac{3}{8})
integral from 0 to 2 of x+2	\int\:_{0}^{2}x+2dx
limit as x approaches 0 of x/((x+0))	\lim\:_{x\to\:0}(\frac{x}{(x+0)})
f^{''}(x)=x^2	f^{\prime\:\prime\:}(x)=x^{2}
derivative of f(x)= 7/(x^9)	derivative\:f(x)=\frac{7}{x^{9}}
integral from 2 to 3 of (23)/(sqrt(3-x))	\int\:_{2}^{3}\frac{23}{\sqrt{3-x}}dx
derivative of f(x)=ln(5x)	derivative\:f(x)=\ln(5x)
limit as x approaches infinity of x*5	\lim\:_{x\to\:\infty\:}(x\cdot\:5)
derivative of (sqrt(x)+c^2)	\frac{d}{dx}((\sqrt{x}+c)^{2})
y^'=((1+x))/(xy^4),y(1)=3	y^{\prime\:}=\frac{(1+x)}{xy^{4}},y(1)=3
derivative of-2x-y^2cos(xy^2-1)	\frac{d}{dx}(-2x-y^{2}\cos(xy^{2})-1)
integral of (4x+1)/(4x^2+2x+3)	\int\:\frac{4x+1}{4x^{2}+2x+3}dx
2t*(dy)/(dt)+5y=sqrt(t)	2t\cdot\:\frac{dy}{dt}+5y=\sqrt{t}
derivative of y=(8x)/(e^x)	derivative\:y=\frac{8x}{e^{x}}
limit as x approaches 1 of e^{5x^3-5x}	\lim\:_{x\to\:1}(e^{5x^{3}-5x})
integral from 0 to 6 of (2x)/((x-7)^2)	\int\:_{0}^{6}\frac{2x}{(x-7)^{2}}dx
derivative of sqrt(5)tan(x)	\frac{d}{dx}(\sqrt{5}\tan(x))
derivative of sin^3(4x)	\frac{d}{dx}(\sin^{3}(4x))
integral of 1/(x(x+0))	\int\:\frac{1}{x(x+0)}dx
d/(dθ)(6/(2-3sin(θ)))	\frac{d}{dθ}(\frac{6}{2-3\sin(θ)})
2y^{''}+y=0	2y^{\prime\:\prime\:}+y=0
integral of sin^3(x/6)	\int\:\sin^{3}(\frac{x}{6})dx
x((dy)/(dx))=y^2-y	x(\frac{dy}{dx})=y^{2}-y
area y=2x,y=2x^3	area\:y=2x,y=2x^{3}
derivative of \sqrt[7]{x}-4/x	\frac{d}{dx}(\sqrt[7]{x}-\frac{4}{x})
derivative of y=5sqrt(7e^{-2x)+6}	derivative\:y=5\sqrt{7e^{-2x}+6}
limit as x approaches 0 of 2x-4	\lim\:_{x\to\:0}(2x-4)
slope of y=-5x^2	slope\:y=-5x^{2}
derivative of (x^2+9^5)	\frac{d}{dx}((x^{2}+9)^{5})
derivative of y=(2x)/(e^x)	derivative\:y=\frac{2x}{e^{x}}
(dy)/(dt)=((4y^2-t^2))/(2ty)	\frac{dy}{dt}=\frac{(4y^{2}-t^{2})}{2ty}
integral of (1/(2x^3)+1/(x^2))	\int\:(\frac{1}{2x^{3}}+\frac{1}{x^{2}})dx
limit as x approaches 0 of 5+9/(x^3)	\lim\:_{x\to\:0}(5+\frac{9}{x^{3}})
(xdy)/(dx)+y=6x+1	\frac{xdy}{dx}+y=6x+1
integral of (csc^2(x))/(cot^7(x))	\int\:\frac{\csc^{2}(x)}{\cot^{7}(x)}dx
derivative of f(x)=(ln(x))/(20+x)	derivative\:f(x)=\frac{\ln(x)}{20+x}
y^'-2y=e^t	y^{\prime\:}-2y=e^{t}
limit as x approaches 4 of sqrt(x^2-10)	\lim\:_{x\to\:4}(\sqrt{x^{2}-10})
limit as x approaches 1 of 6/(x^3-1)	\lim\:_{x\to\:1}(\frac{6}{x^{3}-1})
integral of (-y)	\int\:(-y)dy
limit as x approaches 4-of (x+4)/(x-4)	\lim\:_{x\to\:4-}(\frac{x+4}{x-4})
derivative of (6x-5^4)	\frac{d}{dx}((6x-5)^{4})
area x,2sqrt(x)	area\:x,2\sqrt{x}
integral of cot(40x)	\int\:\cot(40x)dx
(\partial)/(\partial x)(e^{xy}xy)	\frac{\partial\:}{\partial\:x}(e^{xy}xy)
d/(d{x)}({x}{z}+e^{-{x}^2+{y}})	\frac{d}{d{x}}({x}{z}+e^{-{x}^{2}+{y}})

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