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Problemas populares de Cálculo

y^'= 1/2 y	y^{\prime\:}=\frac{1}{2}y
derivative 4^{cos(3t)}	derivative\:4^{\cos(3t)}
laplacetransformación sin(t-pi)	laplacetransform\:\sin(t-π)
integral de (3x)/(x^2-x-2)	\int\:\frac{3x}{x^{2}-x-2}dx
(x-1)dy+(y-x^2+2x^{-3})dx=0	(x-1)dy+(y-x^{2}+2x^{-3})dx=0
área x=y^{1/2},x=2[0,2]	area\:x=y^{\frac{1}{2}},x=2[0,2]
tangent f(x)=x^2,\at x=0.2	tangent\:f(x)=x^{2},\at\:x=0.2
derivative f(x)= 7/(x^2)	derivative\:f(x)=\frac{7}{x^{2}}
integral de 1/3 sec(x)tan(x)	\int\:\frac{1}{3}\sec(x)\tan(x)dx
derivada de-1/(x^2+1)	\frac{d}{dx}(-\frac{1}{x^{2}}+1)
límite cuando x tiende a infinity de 1-1^x	\lim\:_{x\to\:\infty\:}(1-1^{x})
y=(3x^2-4x)e^{5x}	y=(3x^{2}-4x)e^{5x}
integral de 2sin(3x)cos(3x)	\int\:2\sin(3x)\cos(3x)dx
integral de 1/(sqrt(9-x^2))	\int\:\frac{1}{\sqrt{9-x^{2}}}dx
integral de (x^2)arctan(7x)	\int\:(x^{2})\arctan(7x)dx
integral de 2x^2ln(x)	\int\:2x^{2}\ln(x)dx
derivative f(x)=(1+7x^2)(x-x^2)	derivative\:f(x)=(1+7x^{2})(x-x^{2})
pendiente (3,-5),(8,4)	slope\:(3,-5),(8,4)
derivada de cos((1-e^{3x}/(1+e^{3x)}))	\frac{d}{dx}(\cos(\frac{1-e^{3x}}{1+e^{3x}}))
y^'+3y=t+e^{-2t}	y^{\prime\:}+3y=t+e^{-2t}
integral de (x^2arcsin(x))/(sqrt(1-x^2))	\int\:\frac{x^{2}\arcsin(x)}{\sqrt{1-x^{2}}}dx
y^{''}+y=sin(2)(x)	y^{\prime\:\prime\:}+y=\sin(2)(x)
integral de 0 a 4 de sqrt(16-x^2)	\int\:_{0}^{4}\sqrt{16-x^{2}}dx
derivative 1/(x^{19)}	derivative\:\frac{1}{x^{19}}
derivative (t+2t^2)/(1+t^2)	derivative\:\frac{t+2t^{2}}{1+t^{2}}
integral de 1/((e^{x/a)-e^{-x/a})^{-2}}	\int\:\frac{1}{(e^{\frac{x}{a}}-e^{-\frac{x}{a}})^{-2}}dx
integral de e^xcos(6x)	\int\:e^{x}\cos(6x)dx
integral de-1 a 4 de 3x^2+8x-5	\int\:_{-1}^{4}3x^{2}+8x-5dx
(dy}{dx}=\frac{x^2+2y)/x ,y(1)=2	\frac{dy}{dx}=\frac{x^{2}+2y}{x},y(1)=2
integral de (7-5x)/(sqrt(64-49x^2))	\int\:\frac{7-5x}{\sqrt{64-49x^{2}}}dx
integral de ((2x-3))/(sqrt(x^2+6x+4))	\int\:\frac{(2x-3)}{\sqrt{x^{2}+6x+4}}dx
derivative f(x)=e^x+e^{-x}	derivative\:f(x)=e^{x}+e^{-x}
límite cuando t tiende a 0 de (1-cos(t))/t	\lim\:_{t\to\:0}(\frac{1-\cos(t)}{t})
derivada de 4cos(x/2)	\frac{d}{dx}(4\cos(\frac{x}{2}))
y^{''}-3y=0	y^{\prime\:\prime\:}-3y=0
límite cuando x tiende a 0+de arctan(2/x)	\lim\:_{x\to\:0+}(\arctan(\frac{2}{x}))
y^{''}+2y^'+20y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+20y=0,y(0)=1,y^{\prime\:}(0)=0
tangent f(x)=x-5cos(x),\at x=0	tangent\:f(x)=x-5\cos(x),\at\:x=0
serie de n=0 a infinity de (x-10)^n	\sum\:_{n=0}^{\infty\:}(x-10)^{n}
derivative f(x)= 1/(3-x)	derivative\:f(x)=\frac{1}{3-x}
integral de 0 a 3 de 2	\int\:_{0}^{3}2dx
derivative (14)/(ln(x))	derivative\:\frac{14}{\ln(x)}
inversalaplace 7/((s-7)^8)	inverselaplace\:\frac{7}{(s-7)^{8}}
integral de θcsc^2(θ)	\int\:θ\csc^{2}(θ)dθ
integral de 5x-6	\int\:5x-6dx
derivative sqrt(x/(x^2+6))	derivative\:\sqrt{\frac{x}{x^{2}+6}}
[x-yarctan(y/x)]dx+xarctan(y/x)dy=0	[x-y\arctan(\frac{y}{x})]dx+x\arctan(\frac{y}{x})dy=0
integral de 7 a infinity de xe^{-2x}	\int\:_{7}^{\infty\:}xe^{-2x}dx
ty^'+2y=t^2	ty^{\prime\:}+2y=t^{2}
límite cuando x tiende a infinity de (e^{2x-7})/(6x)	\lim\:_{x\to\:\infty\:}(\frac{e^{2x-7}}{6x})
integral de (x^2-7)/(7x)	\int\:\frac{x^{2}-7}{7x}dx
derivative 7e^xsqrt(x)	derivative\:7e^{x}\sqrt{x}
límite cuando x tiende a infinity de 25-2x	\lim\:_{x\to\:\infty\:}(25-2x)
derivative ln\|ln(5x)\|	derivative\:\ln\left\|\ln(5x)\right\|
integral de 4/(xln(9x))	\int\:\frac{4}{x\ln(9x)}dx
integral de (3x^2-2x)	\int\:(3x^{2}-2x)dx
integral de cos(2kx)	\int\:\cos(2kx)dx
derivada de 2-4x^2	\frac{d}{dx}(2-4x^{2})
integral de x/(x^2-x+1)	\int\:\frac{x}{x^{2}-x+1}dx
(dy)/(dx)=(x-y)/(x+2y),y(0)=1	\frac{dy}{dx}=\frac{x-y}{x+2y},y(0)=1
integral de 0 a 2 de 1/((x+1)^4)	\int\:_{0}^{2}\frac{1}{(x+1)^{4}}dx
derivative f(x)=(arccot(x))^5	derivative\:f(x)=(\arccot(x))^{5}
integral de (x+1)(x-2)	\int\:(x+1)(x-2)dx
derivative f(x)=(1-5x)/(4+x)	derivative\:f(x)=\frac{1-5x}{4+x}
(\partial)/(\partial x)(pi^7)	\frac{\partial\:}{\partial\:x}(π^{7})
derivada de 2sin^2(2x)	\frac{d}{dx}(2\sin^{2}(2x))
derivative f(x)= 3/(x-6)	derivative\:f(x)=\frac{3}{x-6}
límite cuando x tiende a-2-de (x^2)/(x+2)	\lim\:_{x\to\:-2-}(\frac{x^{2}}{x+2})
límite cuando n tiende a infinity de n^2	\lim\:_{n\to\:\infty\:}(n^{2})
derivada de e^{-x}*ln(x)	\frac{d}{dx}(e^{-x}\cdot\:\ln(x))
tangent y=2x^3-3x,(1,-1)	tangent\:y=2x^{3}-3x,(1,-1)
4sqrt(xy)((dy)/(dx))=3	4\sqrt{xy}(\frac{dy}{dx})=3
límite cuando x tiende a 0 de b+0^c*ln(0)	\lim\:_{x\to\:0}(b+0^{c}\cdot\:\ln(0))
límite cuando k tiende a infinity de 2k+1	\lim\:_{k\to\:\infty\:}(2k+1)
integral de 0 a 4 de (16-x^2)	\int\:_{0}^{4}(16-x^{2})dx
d/(dy)((x^2)/(y^2+1))	\frac{d}{dy}(\frac{x^{2}}{y^{2}+1})
tangent f(x)=4e^xcos(x),\at x=0	tangent\:f(x)=4e^{x}\cos(x),\at\:x=0
derivative y=(5x^2+4)/(x+3)	derivative\:y=\frac{5x^{2}+4}{x+3}
integral de 0 a pi/4 de xsin(8x)	\int\:_{0}^{\frac{π}{4}}x\sin(8x)dx
maclaurin x^2ln(9+x)	maclaurin\:x^{2}\ln(9+x)
tangent y=sqrt(2x),(32,8)	tangent\:y=\sqrt{2x},(32,8)
integral de cos(14x)cos(5x)	\int\:\cos(14x)\cos(5x)dx
integral de (sqrt(tan(x)+1))/(cos^2(x))	\int\:\frac{\sqrt{\tan(x)+1}}{\cos^{2}(x)}dx
integral de x\sqrt[3]{2x+1}	\int\:x\sqrt[3]{2x+1}dx
(\partial)/(\partial y)(y^5cos(2x))	\frac{\partial\:}{\partial\:y}(y^{5}\cos(2x))
integral de (3x^2)/(sqrt(x^3+8))	\int\:\frac{3x^{2}}{\sqrt{x^{3}+8}}dx
integral de x^2sin(pi)x	\int\:x^{2}\sin(π)xdx
(dy)/(dx)= y/3+3x+7	\frac{dy}{dx}=\frac{y}{3}+3x+7
integral de (-8cos(-2))d	\int\:(-8\cos(-2))ddd
integral de 1/(x^4sqrt(x^2+5))	\int\:\frac{1}{x^{4}\sqrt{x^{2}+5}}dx
(\partial)/(\partial x)(sin(2x+3y+z))	\frac{\partial\:}{\partial\:x}(\sin(2x+3y+z))
límite cuando x tiende a 3 de ln(x+3)	\lim\:_{x\to\:3}(\ln(x+3))
integral de (2x^2-7x-1)/((x-1)(x+1)^2)	\int\:\frac{2x^{2}-7x-1}{(x-1)(x+1)^{2}}dx
y^'=(5x^3+y^3)/(xy^2)	y^{\prime\:}=\frac{5x^{3}+y^{3}}{xy^{2}}
integral de 3cos(sqrt(7x))	\int\:3\cos(\sqrt{7x})dx
y^{''}+49y^'=0	y^{\prime\:\prime\:}+49y^{\prime\:}=0
(\partial)/(\partial a)(cos(a)sin(a+2b))	\frac{\partial\:}{\partial\:a}(\cos(a)\sin(a+2b))
(\partial)/(\partial x)(3x^2-2xy+y^2-8y)	\frac{\partial\:}{\partial\:x}(3x^{2}-2xy+y^{2}-8y)
límite cuando x tiende a infinity de sqrt(x+\sqrt{x)}-sqrt(x-\sqrt{x)}	\lim\:_{x\to\:\infty\:}(\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}})
límite cuando x tiende a 2 de x^3-1	\lim\:_{x\to\:2}(x^{3}-1)

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