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Problemas populares de Cálculo

(x^2+1)dy=(x-4xy)dx	(x^{2}+1)dy=(x-4xy)dx
integral de 22tan^3(x)	\int\:22\tan^{3}(x)dx
integral de 1/(sqrt(1+e^x))	\int\:\frac{1}{\sqrt{1+e^{x}}}dx
integral de (e^x)/(e^x+8)	\int\:\frac{e^{x}}{e^{x}+8}dx
integral de 0 a 1 de 4/(sqrt(x)(1+x))	\int\:_{0}^{1}\frac{4}{\sqrt{x}(1+x)}dx
límite cuando θ tiende a 0 de (2sin(3θ))/θ	\lim\:_{θ\to\:0}(\frac{2\sin(3θ)}{θ})
derivada de 7/(xln(x))	\frac{d}{dx}(\frac{7}{x\ln(x)})
(\partial)/(\partial y)(x^2+z^2)	\frac{\partial\:}{\partial\:y}(x^{2}+z^{2})
(\partial)/(\partial x)(a)	\frac{\partial\:}{\partial\:x}(a)
f(x)=(((x-3))/((x+2)))^2x=-1	f(x)=(\frac{(x-3)}{(x+2)})^{2}x=-1
integral de (e^x)/((e^x+1)^3)	\int\:\frac{e^{x}}{(e^{x}+1)^{3}}dx
y^'=ry(1-y/k)	y^{\prime\:}=ry(1-\frac{y}{k})
derivada de (x^3-2^5)	\frac{d}{dx}((x^{3}-2)^{5})
límite cuando x tiende a 0 de x^{14}ln(x)	\lim\:_{x\to\:0}(x^{14}\ln(x))
derivada de e^{3/2 x}	\frac{d}{dx}(e^{\frac{3}{2}x})
derivada de 1/((x-5^2))	\frac{d}{dx}(\frac{1}{(x-5)^{2}})
integral de (te^ti-4e^{-2t}j+8te^{t^2}k)	\int\:(te^{t}i-4e^{-2t}j+8te^{t^{2}}k)dt
(\partial)/(\partial x)((2x+3)/(4y-1))	\frac{\partial\:}{\partial\:x}(\frac{2x+3}{4y-1})
pendiente (90,62536),(950,9000)	slope\:(90,62536),(950,9000)
d/(dt)((Ae^{mt})/(B+Ce^{mt)})	\frac{d}{dt}(\frac{Ae^{mt}}{B+Ce^{mt}})
(\partial)/(\partial x)(y^2(x+y)^{-2})	\frac{\partial\:}{\partial\:x}(y^{2}(x+y)^{-2})
integral de (tan(x/(14)))^5	\int\:(\tan(\frac{x}{14}))^{5}dx
11xy^'+y=132x	11xy^{\prime\:}+y=132x
derivative (u^{-2}+u^{-3})(u^5-6u^2)	derivative\:(u^{-2}+u^{-3})(u^{5}-6u^{2})
integral de e^{-x}+2	\int\:e^{-x}+2dx
derivada de (9x/((x^2+81)^{3/2)})	\frac{d}{dx}(\frac{9x}{(x^{2}+81)^{\frac{3}{2}}})
derivative (1+4x)^{1/2}	derivative\:(1+4x)^{\frac{1}{2}}
derivada de ((x-1/(x+1))^3)	\frac{d}{dx}((\frac{x-1}{x+1})^{3})
integral de 5x^{15}e^{-x^8}	\int\:5x^{15}e^{-x^{8}}dx
integral de 1/(x(ln(x))^6)	\int\:\frac{1}{x(\ln(x))^{6}}dx
inversalaplace (4s)/((s+1)^2)	inverselaplace\:\frac{4s}{(s+1)^{2}}
derivada de 3x^2+e^2x+pi^2	\frac{d}{dx}(3x^{2}+e^{2}x+π^{2})
integral de 1/(x^2sqrt(x^2+100))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+100}}dx
derivative f(x)=x^8-9e^{3x}	derivative\:f(x)=x^{8}-9e^{3x}
integral de 0 a pi de cos(t)	\int\:_{0}^{π}\cos(t)dt
derivada de 2x^3-12x^2+18x	\frac{d}{dx}(2x^{3}-12x^{2}+18x)
límite cuando x tiende a 3 de (-4)x	\lim\:_{x\to\:3}((-4)x)
(dx)/(dy)+800y=400	\frac{dx}{dy}+800y=400
derivada de (x-3(x^3-2))	\frac{d}{dx}((x-3)(x^{3}-2))
derivada de (ln(5x)^2)	\frac{d}{dx}((\ln(5x))^{2})
(\partial)/(\partial x)((90-x)^2*(x+2))	\frac{\partial\:}{\partial\:x}((90-x)^{2}\cdot\:(x+2))
integral de 3/(2xsqrt(9x^2-1))	\int\:\frac{3}{2x\sqrt{9x^{2}-1}}dx
derivative f(x)=14^x	derivative\:f(x)=14^{x}
integral de 1 a 4 de 1/(x-4)	\int\:_{1}^{4}\frac{1}{x-4}dx
laplacetransformación 4t-10	laplacetransform\:4t-10
integral de 1/(xsqrt(x^2-4))	\int\:\frac{1}{x\sqrt{x^{2}-4}}dx
integral de (\sqrt[3]{x^2})	\int\:(\sqrt[3]{x^{2}})dx
derivative ln((7x^2+8x+5)/(8x^3-1))	derivative\:\ln(\frac{7x^{2}+8x+5}{8x^{3}-1})
derivative f(x)=sqrt(x)e^x\at x	derivative\:f(x)=\sqrt{x}e^{x}\at\:x
integral de \sqrt[8]{x}+\sqrt[9]{x}	\int\:\sqrt[8]{x}+\sqrt[9]{x}dx
integral de 10t	\int\:10tdt
derivative f(x)=(t^6+1)^{500}	derivative\:f(x)=(t^{6}+1)^{500}
2x(dy)/(dx)=2xe^x-2y+6x^2	2x\frac{dy}{dx}=2xe^{x}-2y+6x^{2}
integral de 1/(3-8x)	\int\:\frac{1}{3-8x}dx
tangent-x/((25-x^2)^{1/2)}	tangent\:-\frac{x}{(25-x^{2})^{\frac{1}{2}}}
derivative (125+x)^{-1/3}	derivative\:(125+x)^{-\frac{1}{3}}
y^{''}+2y^'+y=14e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=14e^{-t}
integral de cos^3(3x)	\int\:\cos^{3}(3x)dx
y^'= y/((x^2+1)x)	y^{\prime\:}=\frac{y}{(x^{2}+1)x}
derivada de (20x/(x^2+2))	\frac{d}{dx}(\frac{20x}{x^{2}+2})
límite cuando x tiende a 3 de 2/(x-2)	\lim\:_{x\to\:3}(\frac{2}{x-2})
inversalaplace ((e^{-2s}-2))/s	inverselaplace\:\frac{(e^{-2s}-2)}{s}
integral de xotx^2	\int\:xotx^{2}dx
(\partial)/(\partial x)(1+e^x)	\frac{\partial\:}{\partial\:x}(1+e^{x})
derivada de 1/(x*ln(x^9))	\frac{d}{dx}(\frac{1}{x\cdot\:\ln(x^{9})})
derivada de 2/(3x^3)	\frac{d}{dx}(\frac{2}{3x^{3}})
integral de 8/(x^7)	\int\:\frac{8}{x^{7}}dx
integral de 18x^{17}	\int\:18x^{17}dx
derivative sqrt(x+\sqrt{x+\sqrt{x)}}	derivative\:\sqrt{x+\sqrt{x+\sqrt{x}}}
x^2y^'+xy=1	x^{2}y^{\prime\:}+xy=1
inversalaplace s/((s^2-1^2)(s^2+17))	inverselaplace\:\frac{s}{(s^{2}-1^{2})(s^{2}+17)}
límite cuando x tiende a-infinity de e^x*x	\lim\:_{x\to\:-\infty\:}(e^{x}\cdot\:x)
integral de (x+10)/(x^2+6x+13)	\int\:\frac{x+10}{x^{2}+6x+13}dx
integral de \sqrt[3]{2-3x^2}(-6x)	\int\:\sqrt[3]{2-3x^{2}}(-6x)dx
(\partial)/(\partial x)(-x+y)	\frac{\partial\:}{\partial\:x}(-x+y)
integral de x^2tan^3(x^3)	\int\:x^{2}\tan^{3}(x^{3})dx
(x^2+4)y^'+3xy=x,y(0)=1	(x^{2}+4)y^{\prime\:}+3xy=x,y(0)=1
área 9x^4-9x^2,8x^2	area\:9x^{4}-9x^{2},8x^{2}
integral de 0 a 1/10 de 1/((100x^2+1)^{3/2)}	\int\:_{0}^{\frac{1}{10}}\frac{1}{(100x^{2}+1)^{\frac{3}{2}}}dx
integral de ((sin(x)))/(cos^2(x))	\int\:\frac{(\sin(x))}{\cos^{2}(x)}dx
implicit (dy)/(dx),9xy=5	implicit\:\frac{dy}{dx},9xy=5
inversalaplace (s+5)/((s+2)(s+3))	inverselaplace\:\frac{s+5}{(s+2)(s+3)}
límite cuando x tiende a infinity de 8/x-8	\lim\:_{x\to\:\infty\:}(\frac{8}{x}-8)
derivative y=(cos(x))/(2+sin(x))	derivative\:y=\frac{\cos(x)}{2+\sin(x)}
derivative cos(2x+pi)	derivative\:\cos(2x+π)
5ty^'+(10+5t((2(t-7))/(7t)))y=0	5ty^{\prime\:}+(10+5t(\frac{2(t-7)}{7t}))y=0
(\partial)/(\partial x)(10sin(xy))	\frac{\partial\:}{\partial\:x}(10\sin(xy))
integral de (12sqrt(x)+sqrt(7))	\int\:(12\sqrt{x}+\sqrt{7})dx
límite cuando x tiende a 4 de 1/(x-3)	\lim\:_{x\to\:4}(\frac{1}{x-3})
derivative-(170t)/((t+4)^2)	derivative\:-\frac{170t}{(t+4)^{2}}
límite cuando x tiende a 1+de 3/(1-x)	\lim\:_{x\to\:1+}(\frac{3}{1-x})
(dy)/(dx)=3x+xy	\frac{dy}{dx}=3x+xy
9y^{''}+12y^'+4y=0	9y^{\prime\:\prime\:}+12y^{\prime\:}+4y=0
integral de 0 a 1 de (3x+1)^4	\int\:_{0}^{1}(3x+1)^{4}dx
tangent f(x)= 1/(1+x^2),\at x=2	tangent\:f(x)=\frac{1}{1+x^{2}},\at\:x=2
(dx)/(dt)=x^2+1/49 ,x(0)=1	\frac{dx}{dt}=x^{2}+\frac{1}{49},x(0)=1
(x^2+1)y^'+6x(y-1)=0,y(0)=6	(x^{2}+1)y^{\prime\:}+6x(y-1)=0,y(0)=6
derivative ln(x+1)	derivative\:\ln(x+1)
(d^3)/(dx^3)(sin(7x))	\frac{d^{3}}{dx^{3}}(\sin(7x))
y^{''}+6y^'+9y=0,y(1)=0,y^'(1)=1	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=0,y(1)=0,y^{\prime\:}(1)=1

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