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Problemas populares de Cálculo

(dy)/(dx)= 3/(xy^2)	\frac{dy}{dx}=\frac{3}{xy^{2}}
integral de (cos(sqrt(2)ln(x))ln(x))/x	\int\:\frac{\cos(\sqrt{2}\ln(x))\ln(x)}{x}dx
integral de (x^3+x^2)	\int\:(x^{3}+x^{2})dx
derivative f(x)=sqrt(7+5x)	derivative\:f(x)=\sqrt{7+5x}
(\partial)/(\partial y)(x^2y-xy^3)	\frac{\partial\:}{\partial\:y}(x^{2}y-xy^{3})
(dy)/(dx)=-2xy	\frac{dy}{dx}=-2xy
integral de x^3ex^4+5	\int\:x^{3}ex^{4}+5dx
integral de (sin(2x))/(sin^2(x))	\int\:\frac{\sin(2x)}{\sin^{2}(x)}dx
(\partial)/(\partial t)(e^{pit})	\frac{\partial\:}{\partial\:t}(e^{πt})
serie de n=1 a infinity de (n+1)/(n+2)	\sum\:_{n=1}^{\infty\:}\frac{n+1}{n+2}
límite cuando x tiende a 4 de (x-2)/x	\lim\:_{x\to\:4}(\frac{x-2}{x})
d/(dt)(st)	\frac{d}{dt}(st)
derivada de (3x-1^5(1-3x)^4)	\frac{d}{dx}((3x-1)^{5}(1-3x)^{4})
integral de (x^2)/(1-4x^2)	\int\:\frac{x^{2}}{1-4x^{2}}dx
límite cuando x tiende a infinity de 4*x	\lim\:_{x\to\:\infty\:}(4\cdot\:x)
límite cuando x tiende a+0+de e^{-2/(x^3)}	\lim\:_{x\to\:+0+}(e^{-\frac{2}{x^{3}}})
derivative f(x)=(x^2)/(cos(x))	derivative\:f(x)=\frac{x^{2}}{\cos(x)}
derivative f(x)=tan(5x)	derivative\:f(x)=\tan(5x)
integral de sec^{-1/2}(x)tan^3(x)	\int\:\sec^{-\frac{1}{2}}(x)\tan^{3}(x)dx
integral de cot(13x)	\int\:\cot(13x)dx
integral de sin^3(x)sin(3x)	\int\:\sin^{3}(x)\sin(3x)dx
integral de (3sin(x))/((1+cos(x))^2)	\int\:\frac{3\sin(x)}{(1+\cos(x))^{2}}dx
derivada de (ln(x)(arctan(x)))	\frac{d}{dx}((\ln(x))(\arctan(x)))
serie de n=1 a infinity de (2^n)/(n3^n)	\sum\:_{n=1}^{\infty\:}\frac{2^{n}}{n3^{n}}
integral de (24)/(1+16x^2)	\int\:\frac{24}{1+16x^{2}}dx
serie de n=0 a infinity de (1/2)^nx^n	\sum\:_{n=0}^{\infty\:}(\frac{1}{2})^{n}x^{n}
integral de 2/(1-2x)	\int\:\frac{2}{1-2x}dx
integral de 1/((y+1))	\int\:\frac{1}{(y+1)}dy
integral de cos^7(x)sin^3(x)	\int\:\cos^{7}(x)\sin^{3}(x)dx
derivada de 4x^2sec(2x)	\frac{d}{dx}(4x^{2}\sec(2x))
y^{''}-2y^'+y=((e^x))/((1+x^2))	y^{\prime\:\prime\:}-2y^{\prime\:}+y=\frac{(e^{x})}{(1+x^{2})}
derivative sin(4t)	derivative\:\sin(4t)
derivative 5^{-x}	derivative\:5^{-x}
integral de (38)/((1-x^2)^{3/2)}	\int\:\frac{38}{(1-x^{2})^{\frac{3}{2}}}dx
(\partial)/(\partial x)(((ax+by))/((cx+dy)))	\frac{\partial\:}{\partial\:x}(\frac{(ax+by)}{(cx+dy)})
derivative ((3x+5)(2x-7))/(8x^2-3)	derivative\:\frac{(3x+5)(2x-7)}{8x^{2}-3}
(\partial)/(\partial x)(xy-3f(x,y)-f(x,y)x^2+f(x,y)y)	\frac{\partial\:}{\partial\:x}(xy-3f(x,y)-f(x,y)x^{2}+f(x,y)y)
integral de sqrt(1+3x^2)(6x)	\int\:\sqrt{1+3x^{2}}(6x)dx
integral de cos(x/3)	\int\:\cos(\frac{x}{3})dx
integral de (2x^3+2x^2+6x+9)/(x^3+3x)	\int\:\frac{2x^{3}+2x^{2}+6x+9}{x^{3}+3x}dx
integral de (x^2-8)^5(2x)	\int\:(x^{2}-8)^{5}(2x)dx
(\partial)/(\partial y)(x^2y+(xe^x)/(y^3))	\frac{\partial\:}{\partial\:y}(x^{2}y+\frac{xe^{x}}{y^{3}})
área 2x^2-2x-6,-2,2	area\:2x^{2}-2x-6,-2,2
integral de 0 a 5 de 46216.8x	\int\:_{0}^{5}46216.8xdx
integral de (sin(sqrt(x)))/(2sqrt(x))	\int\:\frac{\sin(\sqrt{x})}{2\sqrt{x}}dx
derivative f(x)=5sqrt(x)sin(x)	derivative\:f(x)=5\sqrt{x}\sin(x)
integral de 0 a pi de cos(2x)	\int\:_{0}^{π}\cos(2x)dx
integral de x/(x^2-3)	\int\:\frac{x}{x^{2}-3}dx
inversalaplace 1/(x(x^2+2x+x))	inverselaplace\:\frac{1}{x(x^{2}+2x+x)}
f(x)=3ln(x)	f(x)=3\ln(x)
derivada de 1/(sqrt(6x+5))	\frac{d}{dx}(\frac{1}{\sqrt{6x+5}})
(\partial)/(\partial y)(7ln(2x^5-3y))	\frac{\partial\:}{\partial\:y}(7\ln(2x^{5}-3y))
área 1/(10x^2),x, x/(10)	area\:\frac{1}{10x^{2}},x,\frac{x}{10}
(dy)/(dx)=ky	\frac{dy}{dx}=ky
(\partial)/(\partial x)(e^x*cos(x))	\frac{\partial\:}{\partial\:x}(e^{x}\cdot\:\cos(x))
derivative 9(x^6-2)^5	derivative\:9(x^{6}-2)^{5}
derivada de (x^2-1/(x+1))	\frac{d}{dx}(\frac{x^{2}-1}{x+1})
derivative f(x)=3x^2+6x	derivative\:f(x)=3x^{2}+6x
límite cuando x tiende a-2 de 3-5x^2	\lim\:_{x\to\:-2}(3-5x^{2})
(\partial)/(\partial x)(1/(2pi)arctan(x/y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2π}\arctan(\frac{x}{y}))
y^'=(xy)/(x^2-1)	y^{\prime\:}=\frac{xy}{x^{2}-1}
pendiente (-7,-9),(1,3)	slope\:(-7,-9),(1,3)
integral de 1 a e^2 de (ln^4(x^2))/x	\int\:_{1}^{e^{2}}\frac{\ln^{4}(x^{2})}{x}dx
taylor ln(1-5y)	taylor\:\ln(1-5y)
inversalaplace 1/(s^2+9s+9)	inverselaplace\:\frac{1}{s^{2}+9s+9}
derivative f(t)=2t^2+3t-6	derivative\:f(t)=2t^{2}+3t-6
(\partial)/(\partial x)(((ax+by))/(cx+dy))	\frac{\partial\:}{\partial\:x}(\frac{(ax+by)}{cx+dy})
xy^{''}+y^'=1	xy^{\prime\:\prime\:}+y^{\prime\:}=1
(\partial)/(\partial x)(6xsin(x+2y-z))	\frac{\partial\:}{\partial\:x}(6x\sin(x+2y-z))
(\partial)/(\partial y)(2x^2+2y-8)	\frac{\partial\:}{\partial\:y}(2x^{2}+2y-8)
integral de (csc^2(x)+4)	\int\:(\csc^{2}(x)+4)dx
derivada de x^2*e^{2x}	\frac{d}{dx}(x^{2}\cdot\:e^{2x})
integral de (2^{2x})/(1+2^{2x)}	\int\:\frac{2^{2x}}{1+2^{2x}}dx
t(dy)/(dt)+4y=t^2	t\frac{dy}{dt}+4y=t^{2}
xy^2y^'=y^3-5x^3,y(1)=2	xy^{2}y^{\prime\:}=y^{3}-5x^{3},y(1)=2
tangent f(x)=-x^2+4	tangent\:f(x)=-x^{2}+4
derivative sin(x)+4/5 cot(x)	derivative\:\sin(x)+\frac{4}{5}\cot(x)
tangent f(x)=3x^2-4x+1,\at x=2	tangent\:f(x)=3x^{2}-4x+1,\at\:x=2
integral de (2u^2-2u^{-1})	\int\:(2u^{2}-2u^{-1})du
3y^{''}+2y^'+y=0	3y^{\prime\:\prime\:}+2y^{\prime\:}+y=0
(\partial)/(\partial y)(y/((x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\frac{y}{(x^{2}+y^{2})})
derivative f(x)=4x^6-7x^5	derivative\:f(x)=4x^{6}-7x^{5}
derivative 5xsin(pix)	derivative\:5x\sin(πx)
integral de (x^3)/(sqrt(x^2+100))	\int\:\frac{x^{3}}{\sqrt{x^{2}+100}}dx
límite cuando t tiende a-2 de (t^3+8)/(t+2)	\lim\:_{t\to\:-2}(\frac{t^{3}+8}{t+2})
derivada de sin(arccos(3x))	\frac{d}{dx}(\sin(\arccos(3x)))
límite cuando x tiende a 3-de 3-x	\lim\:_{x\to\:3-}(3-x)
y^{''}+2y^'=1,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}=1,y(0)=1,y^{\prime\:}(0)=0
integral de 0 a 2 de 4	\int\:_{0}^{2}4dx
integral de (e^x+e^{-x})^2	\int\:(e^{x}+e^{-x})^{2}dx
integral de 0 a pi/3 de 6sec^3(x)	\int\:_{0}^{\frac{π}{3}}6\sec^{3}(x)dx
límite cuando x tiende a-0.001 de (e^x-1)/x	\lim\:_{x\to\:-0.001}(\frac{e^{x}-1}{x})
integral de-2 a 3 de x^3	\int\:_{-2}^{3}x^{3}dx
integral de 1/(sqrt((x^2-1)^3))	\int\:\frac{1}{\sqrt{(x^{2}-1)^{3}}}dx
límite cuando x tiende a 3 de 4x^2	\lim\:_{x\to\:3}(4x^{2})
(\partial)/(\partial x)(acos(x)sin(y))	\frac{\partial\:}{\partial\:x}(a\cos(x)\sin(y))
límite cuando x tiende a 1 de e^{1/(1-x)}	\lim\:_{x\to\:1}(e^{\frac{1}{1-x}})
derivada de 2x^{3/4}	\frac{d}{dx}(2x^{\frac{3}{4}})
(\partial)/(\partial y)(xy+z^2)	\frac{\partial\:}{\partial\:y}(xy+z^{2})
integral de 7xsec^2(x)	\int\:7x\sec^{2}(x)dx

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