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Problemas populares de Cálculo

(d^2x)/(dt)+2(dx)/(dt)+x=1	\frac{d^{2}x}{dt}+2\frac{dx}{dt}+x=1
integral de sqrt(5+x^2)	\int\:\sqrt{5+x^{2}}dx
área y=8x,y=4x^2	area\:y=8x,y=4x^{2}
(\partial)/(\partial y)(2e^xln(y))	\frac{\partial\:}{\partial\:y}(2e^{x}\ln(y))
(\partial)/(\partial x)(4xy+yz+3xz-32)	\frac{\partial\:}{\partial\:x}(4xy+yz+3xz-32)
derivada de x^6e^{2x^3}	\frac{d}{dx}(x^{6}e^{2x^{3}})
maclaurin (1+x^2)^{(-3)/2}	maclaurin\:(1+x^{2})^{\frac{-3}{2}}
y^'=((3y^2+9))/(2xy)	y^{\prime\:}=\frac{(3y^{2}+9)}{2xy}
serie de n=1 a infinity de 1/(2+n)	\sum\:_{n=1}^{\infty\:}\frac{1}{2+n}
límite cuando x tiende a 0 de (1-e^{2x})/x	\lim\:_{x\to\:0}(\frac{1-e^{2x}}{x})
integral de-infinity a 8 de re^{r/2}	\int\:_{-\infty\:}^{8}re^{\frac{r}{2}}dr
d/(dt)(sin(pit))	\frac{d}{dt}(\sin(πt))
(\partial)/(\partial y)(sin^3(x^2y))	\frac{\partial\:}{\partial\:y}(\sin^{3}(x^{2}y))
integral de-1 a 1 de (x^2+1)^2	\int\:_{-1}^{1}(x^{2}+1)^{2}dx
derivative y=e^{-1/2 x}	derivative\:y=e^{-\frac{1}{2}x}
derivative (2x^3+5x)(x-3)(x+2)	derivative\:(2x^{3}+5x)(x-3)(x+2)
derivada de ln(y-x)	\frac{d}{dx}(\ln(y-x))
-x^2+8x-9,(1/2 x)+1,x=3,x=5	-x^{2}+8x-9,(\frac{1}{2}x)+1,x=3,x=5
integral de-infinity a 0 de 1/(7-5x)	\int\:_{-\infty\:}^{0}\frac{1}{7-5x}dx
integral de x^2sqrt((1-x^3)^5)	\int\:x^{2}\sqrt{(1-x^{3})^{5}}dx
derivada de (x^3+x^6)	\frac{d}{dx}((x^{3}+x)^{6})
derivada de x(6^{-2x})	\frac{d}{dx}(x(6^{-2x}))
maclaurin e^{x^4},3	maclaurin\:e^{x^{4}},3
integral de-pi a pi de x^3sin(nx)	\int\:_{-π}^{π}x^{3}\sin(nx)dx
derivative 7-x-x^2	derivative\:7-x-x^{2}
derivada de x/(sqrt(5+x^2))	\frac{d}{dx}(\frac{x}{\sqrt{5+x^{2}}})
y^{''}+9y=4tan(3x)	y^{\prime\:\prime\:}+9y=4\tan(3x)
derivative y=ln^2(x+3)	derivative\:y=\ln^{2}(x+3)
(\partial)/(\partial x)(e^{x^2y})	\frac{\partial\:}{\partial\:x}(e^{x^{2}y})
2y^{''}+12y^'+50y=0,y(0)=0,y^'(0)=-8	2y^{\prime\:\prime\:}+12y^{\prime\:}+50y=0,y(0)=0,y^{\prime\:}(0)=-8
tangent y=sqrt(x+8),(8,4)	tangent\:y=\sqrt{x+8},(8,4)
integral de 8e^t-5	\int\:8e^{t}-5dt
derivative (8x^2+18x)/((9+8x)^2)	derivative\:\frac{8x^{2}+18x}{(9+8x)^{2}}
derivative x^{1/6}	derivative\:x^{\frac{1}{6}}
derivada de-x^2+13x-22	\frac{d}{dx}(-x^{2}+13x-22)
integral de e^{t-st}	\int\:e^{t-st}
pendiente g(x)=10xe^{3-x^2}	slope\:g(x)=10xe^{3-x^{2}}
7t*y^'-5y=sqrt(t)	7t\cdot\:y^{\prime\:}-5y=\sqrt{t}
4y^{''}-y=1,y(0)=0,y^'(0)= 1/2	4y^{\prime\:\prime\:}-y=1,y(0)=0,y^{\prime\:}(0)=\frac{1}{2}
(dy)/(dx)=sqrt((3y-2)/(2x+1))	\frac{dy}{dx}=\sqrt{\frac{3y-2}{2x+1}}
límite cuando x tiende a 2 de (e^3)/x	\lim\:_{x\to\:2}(\frac{e^{3}}{x})
(ln(1/x))^'	(\ln(\frac{1}{x}))^{\prime\:}
tangent 6sqrt(x)	tangent\:6\sqrt{x}
d/(dp)(((10p^{0.25}+1))/(p^{0.25)})	\frac{d}{dp}(\frac{(10p^{0.25}+1)}{p^{0.25}})
integral de 2 a 4 de x^2((2x-3))/6	\int\:_{2}^{4}x^{2}\frac{(2x-3)}{6}dx
límite cuando x tiende a 2+de ax^2-bx+3	\lim\:_{x\to\:2+}(ax^{2}-bx+3)
integral de 0 a 2 de integral de 0 a 1 de xye^{xy^2}	\int\:_{0}^{2}\int\:_{0}^{1}xye^{xy^{2}}dydx
integral de 1/(sqrt(x^2+11))	\int\:\frac{1}{\sqrt{x^{2}+11}}dx
(dP}{dt}=(P/5)(log_{e}(\frac{3000)/P))	\frac{dP}{dt}=(\frac{P}{5})(\log_{e}(\frac{3000}{P}))
(\partial)/(\partial x)(6y^5sin(3x))	\frac{\partial\:}{\partial\:x}(6y^{5}\sin(3x))
derivative y=(x^2+5x+2)^3	derivative\:y=(x^{2}+5x+2)^{3}
límite cuando x tiende a c/(2^-) de [2x-4]	\lim\:_{x\to\:\frac{c}{2^{-}}}([2x-4])
(y^2+xy^2)y^'=1	(y^{2}+xy^{2})y^{\prime\:}=1
derivative g(x)=(3x+1)/((2x^2-5)^2)	derivative\:g(x)=\frac{3x+1}{(2x^{2}-5)^{2}}
laplacetransformación (1+e^t)^2	laplacetransform\:(1+e^{t})^{2}
(\partial)/(\partial x)(8+xln(xy-5))	\frac{\partial\:}{\partial\:x}(8+x\ln(xy-5))
integral de (x^2)/u	\int\:\frac{x^{2}}{u}du
derivative f(x)=x^2arctan(4x)	derivative\:f(x)=x^{2}\arctan(4x)
(\partial)/(\partial y)(e^x+y^2)	\frac{\partial\:}{\partial\:y}(e^{x}+y^{2})
derivative h(x)= 7/(x^2)	derivative\:h(x)=\frac{7}{x^{2}}
inversalaplace ((s+1))/((s*(s^2+s+1)))	inverselaplace\:\frac{(s+1)}{(s\cdot\:(s^{2}+s+1))}
serie de n=5 a infinity de 1/(2^{2n)}	\sum\:_{n=5}^{\infty\:}\frac{1}{2^{2n}}
tangent f(x)=5-8x^2	tangent\:f(x)=5-8x^{2}
(dy)/(dx)=7sqrt(xy)	\frac{dy}{dx}=7\sqrt{xy}
derivada de e^{3x+2y}	\frac{d}{dx}(e^{3x+2y})
derivative f(x)=(7x-8)^2	derivative\:f(x)=(7x-8)^{2}
d/(dy)(y-x)	\frac{d}{dy}(y-x)
integral de (2e^x+4^x)	\int\:(2e^{x}+4^{x})dx
integral de e^{u^2}	\int\:e^{u^{2}}du
integral de (x+2)/(sqrt(x^2+4))	\int\:\frac{x+2}{\sqrt{x^{2}+4}}dx
tangent f(x)= 2/x ,\at x=-2	tangent\:f(x)=\frac{2}{x},\at\:x=-2
y^{''}+y=2^x	y^{\prime\:\prime\:}+y=2^{x}
integral de 1 a 3 de (x^5+1/(4x^5))	\int\:_{1}^{3}(x^{5}+\frac{1}{4x^{5}})dx
integral de 10xe^{-5x}	\int\:10xe^{-5x}dx
tangent f(x)= 3/x ,(-5,-3/5)	tangent\:f(x)=\frac{3}{x},(-5,-\frac{3}{5})
serie de n=0 a infinity de sin(1/n)	\sum\:_{n=0}^{\infty\:}\sin(\frac{1}{n})
integral de x^2sqrt(5x+8)	\int\:x^{2}\sqrt{5x+8}dx
derivative 6(x-3)^{2/3}	derivative\:6(x-3)^{\frac{2}{3}}
integral de 1 a 9 de 1/(x-5)	\int\:_{1}^{9}\frac{1}{x-5}dx
límite cuando x tiende a 0 de xcos(1/x)	\lim\:_{x\to\:0}(x\cos(\frac{1}{x}))
integral de xye^{x+y}	\int\:xye^{x+y}dx
derivada de ((ax+by(x))/((cx+dy)))	\frac{d}{dx}(\frac{(ax+by(x))}{(cx+dy)})
derivative (x^2-2)(x^3-3x)	derivative\:(x^{2}-2)(x^{3}-3x)
integral de (tan(3x))/(cos(3x))	\int\:\frac{\tan(3x)}{\cos(3x)}dx
5y^{''}+y^'=-10x,y(0)=0,y^'(0)=-15	5y^{\prime\:\prime\:}+y^{\prime\:}=-10x,y(0)=0,y^{\prime\:}(0)=-15
tangent f(x)=(2x+1)/(x+2),(1,1)	tangent\:f(x)=\frac{2x+1}{x+2},(1,1)
integral de (x*(sqrt(1-x^4)))	\int\:(x\cdot\:(\sqrt{1-x^{4}}))dx
(dy)/(dx)=y^2x^3	\frac{dy}{dx}=y^{2}x^{3}
integral de 2/(2+e^x)	\int\:\frac{2}{2+e^{x}}dx
límite cuando x tiende a 3 de 7-3x	\lim\:_{x\to\:3}(7-3x)
(\partial)/(\partial x)(-3x^2-4x)	\frac{\partial\:}{\partial\:x}(-3x^{2}-4x)
límite cuando x tiende a 0+de 1-ln(x)	\lim\:_{x\to\:0+}(1-\ln(x))
inversalaplace 3/((s^2+1)(s^2+9))	inverselaplace\:\frac{3}{(s^{2}+1)(s^{2}+9)}
integral de (3x^2+2x+1)/(x^2(x+1))	\int\:\frac{3x^{2}+2x+1}{x^{2}(x+1)}dx
integral de-sin^2(x)+cos^2(x)	\int\:-\sin^{2}(x)+\cos^{2}(x)dx
integral de 1 a 3 de (sqrt(x^2-1))/x	\int\:_{1}^{3}\frac{\sqrt{x^{2}-1}}{x}dx
integral de arctan(sqrt(\sqrt{x)-1})	\int\:\arctan(\sqrt{\sqrt{x}-1})dx
integral de 1/((x^3-1))	\int\:\frac{1}{(x^{3}-1)}dx
integral de (2x^2-1)/(x(x+1)^3)	\int\:\frac{2x^{2}-1}{x(x+1)^{3}}dx
derivada de tan(sqrt(1-x))	\frac{d}{dx}(\tan(\sqrt{1-x}))

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