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Problemas populares de Cálculo

y^{''}+4y^'+6y=0,y(0)=-4,y^'(0)=-1	y^{\prime\:\prime\:}+4y^{\prime\:}+6y=0,y(0)=-4,y^{\prime\:}(0)=-1
inversalaplace (x+1)/(x^2-4x)	inverselaplace\:\frac{x+1}{x^{2}-4x}
integral de csc^2(x)+7	\int\:\csc^{2}(x)+7dx
límite cuando x tiende a 6 de x^2-7x+6	\lim\:_{x\to\:6}(x^{2}-7x+6)
(\partial)/(\partial x)(5yln(x))	\frac{\partial\:}{\partial\:x}(5y\ln(x))
derivada de (x^3/(3-x^2))	\frac{d}{dx}(\frac{x^{3}}{3-x^{2}})
derivative 1/(2sqrt(x+10))	derivative\:\frac{1}{2\sqrt{x+10}}
y^'=2xe^y	y^{\prime\:}=2xe^{y}
(\partial)/(\partial x)(e^{xy}cos(bx+c))	\frac{\partial\:}{\partial\:x}(e^{xy}\cos(bx+c))
(dy)/(dx)=2+sqrt(y-2x+4)	\frac{dy}{dx}=2+\sqrt{y-2x+4}
implicit (dy)/(dx),2xy=6	implicit\:\frac{dy}{dx},2xy=6
pendiente (8.3)(3.5)	slope\:(8.3)(3.5)
integral de (x^2+4)^53x	\int\:(x^{2}+4)^{5}3xdx
(\partial)/(\partial x)(5x^2-3xy+xyz)	\frac{\partial\:}{\partial\:x}(5x^{2}-3xy+xyz)
pendiente-2t^3	slope\:-2t^{3}
integral de x/(sqrt(x^2-2x))	\int\:\frac{x}{\sqrt{x^{2}-2x}}dx
límite cuando x tiende a 0 de x^2sin(x)	\lim\:_{x\to\:0}(x^{2}\sin(x))
integral de-5sin(5t)	\int\:-5\sin(5t)dt
derivative y^3	derivative\:y^{3}
integral de 0 a x de sin^2(t)	\int\:_{0}^{x}\sin^{2}(t)dt
implicit (dx)/(dy),y^2-x=0	implicit\:\frac{dx}{dy},y^{2}-x=0
tangent f(x)=x^4+8x^3-2x-2,\at x=-2	tangent\:f(x)=x^{4}+8x^{3}-2x-2,\at\:x=-2
integral de (sec^2(x))/(sqrt(1+tan(x)))	\int\:\frac{\sec^{2}(x)}{\sqrt{1+\tan(x)}}dx
((e^x+e^{-x})dy)/(dx)=y^2	\frac{(e^{x}+e^{-x})dy}{dx}=y^{2}
derivada de 1/(sqrt(x^2-9))	\frac{d}{dx}(\frac{1}{\sqrt{x^{2}-9}})
derivada de \sqrt[4]{x^5-x^3-2}	\frac{d}{dx}(\sqrt[4]{x^{5}-x^{3}-2})
integral de 3xe^{4x}	\int\:3xe^{4x}dx
derivada de x/((x^2+1^{1/2)}-1)	\frac{d}{dx}(\frac{x}{(x^{2}+1)^{\frac{1}{2}}}-1)
derivative sqrt(s^2+t^2)	derivative\:\sqrt{s^{2}+t^{2}}
integral de e^{cos(pix)}sin(pix)	\int\:e^{\cos(πx)}\sin(πx)dx
serie de n=0 a infinity de (n)sin(1/n)	\sum\:_{n=0}^{\infty\:}(n)\sin(\frac{1}{n})
y^'+ay-b=0	y^{\prime\:}+ay-b=0
integral de 5/(4+9r^2)	\int\:\frac{5}{4+9r^{2}}dr
límite cuando x tiende a infinity de 4+x	\lim\:_{x\to\:\infty\:}(4+x)
integral de ((x+3))/((x+4))	\int\:\frac{(x+3)}{(x+4)}dx
derivada de 4x^3+3x^2+2x+1	\frac{d}{dx}(4x^{3}+3x^{2}+2x+1)
derivative y=2x^2-5	derivative\:y=2x^{2}-5
serie de n=1 a infinity de 5^{1/n}	\sum\:_{n=1}^{\infty\:}5^{\frac{1}{n}}
integral de tan^9(x)sec^2(x)	\int\:\tan^{9}(x)\sec^{2}(x)dx
integral de 2 a 6 de (x-4)/(x+1)	\int\:_{2}^{6}\frac{x-4}{x+1}dx
integral de x^2*ln(6x)	\int\:x^{2}\cdot\:\ln(6x)dx
derivada de (8x+15^{12}(x^3+7)^{13})	\frac{d}{dx}((8x+15)^{12}(x^{3}+7)^{13})
integral de (x-9x^2)/(sqrt(x))	\int\:\frac{x-9x^{2}}{\sqrt{x}}dx
(dy)/(3x+e^x)=e^{-y}dx	\frac{dy}{3x+e^{x}}=e^{-y}dx
desarrollar csc(x)(x+cot(x))	expand\:\csc(x)(x+\cot(x))
derivative x^7e^x	derivative\:x^{7}e^{x}
(dy)/(dx)=2y+a	\frac{dy}{dx}=2y+a
integral de 1/(z+1)	\int\:\frac{1}{z+1}
derivada de-(x^2)	\frac{d}{dx}(-(x^{2}))
derivada de (-11/(sqrt(x)))	\frac{d}{dx}(\frac{-11}{\sqrt{x}})
límite cuando x tiende a 0+de ((sin(x))/x)^{1/x}	\lim\:_{x\to\:0+}((\frac{\sin(x)}{x})^{\frac{1}{x}})
derivada de (1+ln(x)/(x^2-ln(x)))	\frac{d}{dx}(\frac{1+\ln(x)}{x^{2}-\ln(x)})
integral de 1/2 x^2ln(x)-(x^2)/4-(x^2)/2	\int\:\frac{1}{2}x^{2}\ln(x)-\frac{x^{2}}{4}-\frac{x^{2}}{2}dx
integral de \sqrt[3]{1-x^2}x	\int\:\sqrt[3]{1-x^{2}}xdx
integral de sqrt(cos(x))sin(x)	\int\:\sqrt{\cos(x)}\sin(x)dx
límite cuando x tiende a-5 de (\|x+5\|)/(x+5)	\lim\:_{x\to\:-5}(\frac{\left\|x+5\right\|}{x+5})
área y= 4/x ,y= 4/(x^2),x=5	area\:y=\frac{4}{x},y=\frac{4}{x^{2}},x=5
integral de sqrt(1+1/x)	\int\:\sqrt{1+\frac{1}{x}}dx
derivada de 6e^{5x}+e^{-x^2}	\frac{d}{dx}(6e^{5x}+e^{-x^{2}})
área x^2,4x-x^2	area\:x^{2},4x-x^{2}
integral de 1/(25e^{-4x)+e^{4x}}	\int\:\frac{1}{25e^{-4x}+e^{4x}}dx
derivative f(x)=(5x^6+2x^3)^4	derivative\:f(x)=(5x^{6}+2x^{3})^{4}
integral de 1/(-x-1)	\int\:\frac{1}{-x-1}dx
(\partial)/(\partial x)(2(x-y)e^{2y+5x^2})	\frac{\partial\:}{\partial\:x}(2(x-y)e^{2y+5x^{2}})
f^'(t)-f(t)=-7t,f(2)=-4	f^{\prime\:}(t)-f(t)=-7t,f(2)=-4
integral de (2y)/(x^2+y^2)	\int\:\frac{2y}{x^{2}+y^{2}}dx
integral de e^{sin(pix)}cos(pix)	\int\:e^{\sin(πx)}\cos(πx)dx
integral de 0 a 3 de (-6)/(xsqrt(x))	\int\:_{0}^{3}\frac{-6}{x\sqrt{x}}dx
(1-5y+x)y^'+y=5x-1	(1-5y+x)y^{\prime\:}+y=5x-1
(1/x)^'	(\frac{1}{x})^{\prime\:}
integral de 9xcos(x)	\int\:9x\cos(x)dx
(dy)/(dx)= 1/y	\frac{dy}{dx}=\frac{1}{y}
derivative f(x)=x^3(x-8)^2	derivative\:f(x)=x^{3}(x-8)^{2}
(dy)/(dx)=e^{2y}sin(3x)	\frac{dy}{dx}=e^{2y}\sin(3x)
tangent f(x)= 7/x ,\at x=1	tangent\:f(x)=\frac{7}{x},\at\:x=1
(\partial)/(\partial x)((x)^2y)	\frac{\partial\:}{\partial\:x}((x)^{2}y)
integral de x^2(3-2x)	\int\:x^{2}(3-2x)dx
área x^2-6x,0	area\:x^{2}-6x,0
integral de pi/4 a pi/3 de cot(x)	\int\:_{\frac{π}{4}}^{\frac{π}{3}}\cot(x)dx
integral de xe^{-7x}	\int\:xe^{-7x}dx
(\partial)/(\partial z)(ze^{xy})	\frac{\partial\:}{\partial\:z}(ze^{xy})
derivative 2+0.55sin((2pit)/(6.2))	derivative\:2+0.55\sin(\frac{2πt}{6.2})
límite cuando x tiende a infinity de 10x	\lim\:_{x\to\:\infty\:}(10x)
integral de 12xln(5x)	\int\:12x\ln(5x)dx
límite cuando x tiende a-3-de 2x^2-6	\lim\:_{x\to\:-3-}(2x^{2}-6)
integral de (6x^2+x-1)/(3x^3-9x^2+x-3)	\int\:\frac{6x^{2}+x-1}{3x^{3}-9x^{2}+x-3}dx
derivative tan(e^{6t})+e^{tan(6t)}	derivative\:\tan(e^{6t})+e^{\tan(6t)}
integral de-e^{2t}+te^t	\int\:-e^{2t}+te^{t}dt
integral de 0 a 1 de xsqrt(6-x^2)	\int\:_{0}^{1}x\sqrt{6-x^{2}}dx
derivada de sin(x+3/4 cot(x))	\frac{d}{dx}(\sin(x)+\frac{3}{4}\cot(x))
(\partial)/(\partial x)(cos(xy^2))	\frac{\partial\:}{\partial\:x}(\cos(xy^{2}))
y^{''}+4y=e^{(-t)}	y^{\prime\:\prime\:}+4y=e^{(-t)}
derivative csc(sqrt(x+5))	derivative\:\csc(\sqrt{x+5})
(dy}{dx}-(\frac{1+x)/x)y=(y^2)/x	\frac{dy}{dx}-(\frac{1+x}{x})y=\frac{y^{2}}{x}
integral de 1 a 3 de 4	\int\:_{1}^{3}4dx
derivative f(x)=sin(2x^3)	derivative\:f(x)=\sin(2x^{3})
integral de 1 a 2 de xsqrt(x^2-1)	\int\:_{1}^{2}x\sqrt{x^{2}-1}dx
H'=((a_{0})/(e^{f(x))}+cos(f(x)))*H	H\prime\:=(\frac{a_{0}}{e^{f(x)}}+\cos(f(x)))\cdot\:H
límite cuando x tiende a infinity de x-3x^4	\lim\:_{x\to\:\infty\:}(x-3x^{4})
derivative 11sqrt(x)-8/x	derivative\:11\sqrt{x}-\frac{8}{x}

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