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Problemas populares de Cálculo

y^{''}+196y=0	y^{\prime\:\prime\:}+196y=0
integral de x^2cosh(x)	\int\:x^{2}\cosh(x)dx
integral de 5/(3+7x^2)	\int\:\frac{5}{3+7x^{2}}dx
integral de (cos(x))(ln(sin(x)))	\int\:(\cos(x))(\ln(\sin(x)))dx
d/(dt)(t/(sqrt(t^2+1)))	\frac{d}{dt}(\frac{t}{\sqrt{t^{2}+1}})
límite cuando x tiende a 1 de x^2-8x-1	\lim\:_{x\to\:1}(x^{2}-8x-1)
derivative f(x)=(e^x)/(3+e^x)	derivative\:f(x)=\frac{e^{x}}{3+e^{x}}
límite cuando x tiende a 3-de sqrt(x^2-9)	\lim\:_{x\to\:3-}(\sqrt{x^{2}-9})
área y=3(x+1),y=4(x+1),x=6	area\:y=3(x+1),y=4(x+1),x=6
integral de (-341x+342)/(x^2+x-2)	\int\:\frac{-341x+342}{x^{2}+x-2}dx
(\partial)/(\partial x)(3xsin(9x^2y))	\frac{\partial\:}{\partial\:x}(3x\sin(9x^{2}y))
límite cuando x tiende a infinity de (1+x)^{3/x}	\lim\:_{x\to\:\infty\:}((1+x)^{\frac{3}{x}})
integral de 1/(x^2+36)	\int\:\frac{1}{x^{2}+36}dx
límite cuando x tiende a-infinity de (x^2+2)/(x^3+x^2-1)	\lim\:_{x\to\:-\infty\:}(\frac{x^{2}+2}{x^{3}+x^{2}-1})
límite cuando x tiende a 0 de 7x^3+1/4 x^2	\lim\:_{x\to\:0}(7x^{3}+\frac{1}{4}x^{2})
(\partial)/(\partial y)(x*ln(x+2y)+x/y)	\frac{\partial\:}{\partial\:y}(x\cdot\:\ln(x+2y)+\frac{x}{y})
tangent f(x)= 1/(x+2)	tangent\:f(x)=\frac{1}{x+2}
límite cuando x tiende a 0 de 2x(1-x)	\lim\:_{x\to\:0}(2x(1-x))
integral de 1 a infinity de x^{-1/2}	\int\:_{1}^{\infty\:}x^{-\frac{1}{2}}dx
integral de ((u-1))/((u+1))	\int\:\frac{(u-1)}{(u+1)}du
serie de n=1 a infinity de 6 1/n	\sum\:_{n=1}^{\infty\:}6\frac{1}{n}
tangent f(x)=x^2+3x+4pi,\at x=-3	tangent\:f(x)=x^{2}+3x+4π,\at\:x=-3
derivada de arccos(x/b)	\frac{d}{dx}(\arccos(\frac{x}{b}))
(d^4)/(dx^4)((8x)/(1-x))	\frac{d^{4}}{dx^{4}}(\frac{8x}{1-x})
derivative f(x)=5^{5x+1}+3^{1-3x}	derivative\:f(x)=5^{5x+1}+3^{1-3x}
y^'+5y=7	y^{\prime\:}+5y=7
(d^2)/(dx^2)(-2x^4-2x^3+60x^2-22)	\frac{d^{2}}{dx^{2}}(-2x^{4}-2x^{3}+60x^{2}-22)
derivada de 2xcos(x-2sin(x))	\frac{d}{dx}(2x\cos(x)-2\sin(x))
tangent x/(1+x^2),\at x=2	tangent\:\frac{x}{1+x^{2}},\at\:x=2
integral de 0.02e^x	\int\:0.02e^{x}dx
2xy^2+4=2(3-x^2y)y^',y(-1)=8	2xy^{2}+4=2(3-x^{2}y)y^{\prime\:},y(-1)=8
derivada de x^3+3x^2-144x	\frac{d}{dx}(x^{3}+3x^{2}-144x)
pendiente (-1.4)(-4.2)	slope\:(-1.4)(-4.2)
integral de 1/(sqrt(4x^2-4x+3))	\int\:\frac{1}{\sqrt{4x^{2}-4x+3}}dx
derivada de x^3-1/(12x)	\frac{d}{dx}(x^{3}-\frac{1}{12x})
taylor 5/(x^3),-1	taylor\:\frac{5}{x^{3}},-1
(\partial)/(\partial x)(-2ycos(6x))	\frac{\partial\:}{\partial\:x}(-2y\cos(6x))
(\partial)/(\partial y)(1/(x^2)+1/(y^2))	\frac{\partial\:}{\partial\:y}(\frac{1}{x^{2}}+\frac{1}{y^{2}})
(\partial)/(\partial u(v))((e^v)/(u(v)+v^6))	\frac{\partial\:}{\partial\:u(v)}(\frac{e^{v}}{u(v)+v^{6}})
derivada de 2/(1-2x)	\frac{d}{dx}(\frac{2}{1-2x})
(\partial)/(\partial x)(x/(2x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{2x^{2}+y^{2}})
integral de x^3*e^{12x}	\int\:x^{3}\cdot\:e^{12x}dx
derivative x^3+3x^2	derivative\:x^{3}+3x^{2}
derivative e^{sin(2x)}+sin(e^{2x})	derivative\:e^{\sin(2x)}+\sin(e^{2x})
taylor 1/(1+x^3),0	taylor\:\frac{1}{1+x^{3}},0
derivada de 2e^{4x^2}	\frac{d}{dx}(2e^{4x^{2}})
inversalaplace 1/(4s^3)	inverselaplace\:\frac{1}{4s^{3}}
límite cuando x tiende a 1 de (x-1)/(1-x)	\lim\:_{x\to\:1}(\frac{x-1}{1-x})
integral de 1/((x^2+2x+3)^2)	\int\:\frac{1}{(x^{2}+2x+3)^{2}}dx
derivada de 4/(sqrt(1-x))	\frac{d}{dx}(\frac{4}{\sqrt{1-x}})
derivada de sin(x+xcos(x))	\frac{d}{dx}(\sin(x)+x\cos(x))
laplacetransformación 7t^2	laplacetransform\:7t^{2}
integral de-pi/4 a pi/4 de cos(x)	\int\:_{-\frac{π}{4}}^{\frac{π}{4}}\cos(x)dx
derivative (6x^2+7)(x^2-1/x)	derivative\:(6x^{2}+7)(x^{2}-\frac{1}{x})
integral de (x^2-x+9)/((x^2+9)^2)	\int\:\frac{x^{2}-x+9}{(x^{2}+9)^{2}}dx
integral de cos(2x)2	\int\:\cos(2x)2dx
límite cuando x tiende a-5+de (x-5)/(x+5)	\lim\:_{x\to\:-5+}(\frac{x-5}{x+5})
(dx)/(dt)=375-(3x)/(800+2t)	\frac{dx}{dt}=375-\frac{3x}{800+2t}
derivative (x^4)/(12)	derivative\:\frac{x^{4}}{12}
y^'=((y^2+xy-x^2))/(x^2)	y^{\prime\:}=\frac{(y^{2}+xy-x^{2})}{x^{2}}
derivative 1/(3x+2)	derivative\:\frac{1}{3x+2}
tangent tan(x)	tangent\:\tan(x)
derivada de 10xe^{-x}	\frac{d}{dx}(10xe^{-x})
(dy)/(dx)=(2x^3)/(y^2)	\frac{dy}{dx}=\frac{2x^{3}}{y^{2}}
(dy)/(dt)+2y=e^{t/3}	\frac{dy}{dt}+2y=e^{\frac{t}{3}}
integral de 17tan^2(x)sec^3(x)	\int\:17\tan^{2}(x)\sec^{3}(x)dx
derivada de (1+sec(x)/(1-sec(x)))	\frac{d}{dx}(\frac{1+\sec(x)}{1-\sec(x)})
derivative ln(t^3)	derivative\:\ln(t^{3})
y^'=(y^2+x^2)/(2xy)	y^{\prime\:}=\frac{y^{2}+x^{2}}{2xy}
cos(x)y^'+sin(x)y=0	\cos(x)y^{\prime\:}+\sin(x)y=0
derivative x^2+24x+c	derivative\:x^{2}+24x+c
derivada de 100x	\frac{d}{dx}(100x)
integral de (2x^3)/(x^2+1)	\int\:\frac{2x^{3}}{x^{2}+1}dx
límite cuando x tiende a 0 de x*ln(x)	\lim\:_{x\to\:0}(x\cdot\:\ln(x))
integral de 2/(1+2x)	\int\:\frac{2}{1+2x}dx
d/(du)(u/(u+v))	\frac{d}{du}(\frac{u}{u+v})
(\partial)/(\partial x)(8yzln(x))	\frac{\partial\:}{\partial\:x}(8yz\ln(x))
límite cuando x tiende a 0 de x^2-5	\lim\:_{x\to\:0}(x^{2}-5)
y^{''}+20y^'+200y=300	y^{\prime\:\prime\:}+20y^{\prime\:}+200y=300
derivada de x^3-27x	\frac{d}{dx}(x^{3}-27x)
integral de sin(ln(t))	\int\:\sin(\ln(t))dt
integral de (sin(sqrt(1+x)))/(sqrt(1+x))	\int\:\frac{\sin(\sqrt{1+x})}{\sqrt{1+x}}dx
derivada de sin((1-e^{2x}/(1+e^{2x)}))	\frac{d}{dx}(\sin(\frac{1-e^{2x}}{1+e^{2x}}))
integral de 2t+3	\int\:2t+3dt
xy^'+y+x=0	xy^{\prime\:}+y+x=0
área (x-3)x(x+3),3-x,0,2	area\:(x-3)x(x+3),3-x,0,2
pendiente y=-(x+1/2)^2+7/2	slope\:y=-(x+\frac{1}{2})^{2}+\frac{7}{2}
integral de 3cos((npix)/3)	\int\:3\cos(\frac{nπx}{3})dx
y^'=(x^2)/(y(2+x^3))	y^{\prime\:}=\frac{x^{2}}{y(2+x^{3})}
(\partial)/(\partial x)(3e^xcos(y))	\frac{\partial\:}{\partial\:x}(3e^{x}\cos(y))
derivada de (x-4^2x^2)	\frac{d}{dx}((x-4)^{2}x^{2})
(\partial)/(\partial x)(-(9x^2)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(-\frac{9x^{2}}{x^{2}+y^{2}})
integral de 4 a 4 de e^{-x^2}	\int\:_{4}^{4}e^{-x^{2}}dx
d/(dy)(sqrt(3x+4y))	\frac{d}{dy}(\sqrt{3x+4y})
inversalaplace (-(16))/((5(x^2+8x+25)))	inverselaplace\:\frac{-(16)}{(5(x^{2}+8x+25))}
integral de 2/(cos(x))	\int\:\frac{2}{\cos(x)}dx
integral de-2 a cos(x) de 3t	\int\:_{-2}^{\cos(x)}3tdt
integral de x(2x+3)	\int\:x(2x+3)dx
pendiente (3)(0.4)	slope\:(3)(0.4)
límite cuando x tiende a-1-de (x+1)/(\|x+1\|)	\lim\:_{x\to\:-1-}(\frac{x+1}{\left\|x+1\right\|})

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