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Problemas populares de Cálculo

(dy)/(dt)+1/t y= 6/t	\frac{dy}{dt}+\frac{1}{t}y=\frac{6}{t}
integral de 1/(sin^2(x)cos(x))	\int\:\frac{1}{\sin^{2}(x)\cos(x)}dx
área 2x,4x^2	area\:2x,4x^{2}
integral de (sin(x))^4(cos(x))^2	\int\:(\sin(x))^{4}(\cos(x))^{2}dx
(\partial)/(\partial x)(xln(x/y))	\frac{\partial\:}{\partial\:x}(x\ln(\frac{x}{y}))
integral de cos(2x)sin(x)	\int\:\cos(2x)\sin(x)dx
integral de (\|x\|+1)	\int\:(\left\|x\right\|+1)dx
taylor (x^2)/(1+x),0	taylor\:\frac{x^{2}}{1+x},0
8(sin(t)y^'+cos(t)y)=cos(t)sin^5(t)	8(\sin(t)y^{\prime\:}+\cos(t)y)=\cos(t)\sin^{5}(t)
derivative 1/(1+5x^2)	derivative\:\frac{1}{1+5x^{2}}
tangent f(x)=sqrt(5x+1),\at x=7	tangent\:f(x)=\sqrt{5x+1},\at\:x=7
derivative e^{-3x}	derivative\:e^{-3x}
derivative f(x)=x^2cot(x)	derivative\:f(x)=x^{2}\cot(x)
integral de cos(ln(x))	\int\:\cos(\ln(x))dx
integral de (x^2)/(sqrt(49+x^2))	\int\:\frac{x^{2}}{\sqrt{49+x^{2}}}dx
integral de x(1+x^3)	\int\:x(1+x^{3})dx
y^'+y=2,y(0)=0	y^{\prime\:}+y=2,y(0)=0
pendiente (-5.3)(7.9)	slope\:(-5.3)(7.9)
integral de 0 a 1 de 5xe^{-x^2}	\int\:_{0}^{1}5xe^{-x^{2}}dx
x^2y^{''}=2xy^'+(y^')^2	x^{2}y^{\prime\:\prime\:}=2xy^{\prime\:}+(y^{\prime\:})^{2}
tangent f(x)=x^2+8,(1,9)	tangent\:f(x)=x^{2}+8,(1,9)
derivada de (4x^3/(x^4+27))	\frac{d}{dx}(\frac{4x^{3}}{x^{4}+27})
derivada de arcsin(tan(sqrt(x^2+1)))	\frac{d}{dx}(\arcsin(\tan(\sqrt{x^{2}+1})))
(\partial)/(\partial x)(ln(x^8y))	\frac{\partial\:}{\partial\:x}(\ln(x^{8}y))
límite cuando x tiende a 0 de-1/(x^2)	\lim\:_{x\to\:0}(-\frac{1}{x^{2}})
derivada de 3sin^2(2x)	\frac{d}{dx}(3\sin^{2}(2x))
integral de (sin^2(x))/(1+cos^2(x))	\int\:\frac{\sin^{2}(x)}{1+\cos^{2}(x)}dx
integral de 15x^3e^x	\int\:15x^{3}e^{x}dx
límite cuando x tiende a infinity de-x	\lim\:_{x\to\:\infty\:}(-x)
derivada de 8xarcsin(x)	\frac{d}{dx}(8x\arcsin(x))
derivada de 3xln(9x^2)	\frac{d}{dx}(3x\ln(9x^{2}))
límite cuando x tiende a 0 de e^{(1/x)}	\lim\:_{x\to\:0}(e^{(\frac{1}{x})})
integral de (1+(1/2)2/((2x+3)))	\int\:(1+(\frac{1}{2})\cdot\:\frac{2}{(2\cdot\:x+3)})dx
derivada de (sin(x^2)/(sin^2(x)))	\frac{d}{dx}(\frac{\sin(x^{2})}{\sin^{2}(x)})
derivative y=6x^2e^{-x}	derivative\:y=6x^{2}e^{-x}
derivative f(x)=2^{20}	derivative\:f(x)=2^{20}
derivative f(x)=2-x	derivative\:f(x)=2-x
derivada de ((3x^2-5^4)/((4x^3+2)^5))	\frac{d}{dx}(\frac{(3x^{2}-5)^{4}}{(4x^{3}+2)^{5}})
derivative y=-x^2+4x	derivative\:y=-x^{2}+4x
y^{''}+2y^'+y=sin(x)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=\sin(x)
integral de (x^4+2x^2-1)/(sqrt(x))	\int\:\frac{x^{4}+2x^{2}-1}{\sqrt{x}}dx
derivada de (sin(x+cos(x))/(x^3+x-2))	\frac{d}{dx}(\frac{\sin(x)+\cos(x)}{x^{3}+x-2})
serie de n=21 a infinity de e^{-0.06n}	\sum\:_{n=21}^{\infty\:}e^{-0.06n}
(x^2-9)(dy)/(dx)+xy=0	(x^{2}-9)\frac{dy}{dx}+xy=0
integral de sqrt(16-4x^2)	\int\:\sqrt{16-4x^{2}}dx
derivative 1/2 sec(2x)	derivative\:\frac{1}{2}\sec(2x)
(dy)/(dx)-y/x =2x^2ln(x)	\frac{dy}{dx}-\frac{y}{x}=2x^{2}\ln(x)
límite cuando x tiende a 1 de 4x^2-2x+5	\lim\:_{x\to\:1}(4x^{2}-2x+5)
derivada de (1+1/x /(1-1/x))	\frac{d}{dx}(\frac{1+\frac{1}{x}}{1-\frac{1}{x}})
(dy)/(dx)=e^{3x}*e^{2y}	\frac{dy}{dx}=e^{3x}\cdot\:e^{2y}
límite cuando x tiende a 3 de (x^2+3)/(x-1)	\lim\:_{x\to\:3}(\frac{x^{2}+3}{x-1})
integral de x^2sqrt(x^3+31)	\int\:x^{2}\sqrt{x^{3}+31}dx
área y= 3/x ,y= x/(12),1<= x<= 6	area\:y=\frac{3}{x},y=\frac{x}{12},1\le\:x\le\:6
límite cuando x tiende a 0 de-1+1/x	\lim\:_{x\to\:0}(-1+\frac{1}{x})
integral de 2 a 3 de (16)/(sqrt(3-x))	\int\:_{2}^{3}\frac{16}{\sqrt{3-x}}dx
maclaurin 1/(2x-5)	maclaurin\:\frac{1}{2x-5}
integral de 1+cot^2(x)	\int\:1+\cot^{2}(x)dx
derivada de (x^3/6-3x)	\frac{d}{dx}(\frac{x^{3}}{6}-3x)
integral de 1/36 x	\int\:\frac{1}{36}xdx
integral de 0 a 4 de 1/(x^2-2x-3)	\int\:_{0}^{4}\frac{1}{x^{2}-2x-3}dx
(dy)/(dx)=(2x)/(x^2+3)(y-1)	\frac{dy}{dx}=\frac{2x}{x^{2}+3}(y-1)
derivative 1/(g^2(x))	derivative\:\frac{1}{g^{2}(x)}
derivative 10x(x^2+5)^4	derivative\:10x(x^{2}+5)^{4}
derivative y=2e^3t	derivative\:y=2e^{3}t
integral de (4x(sqrt(3x)-2))	\int\:(4x(\sqrt{3x}-2))dx
derivada de 2aarccos(sqrt(2x))	\frac{d}{dx}(2a\arccos(\sqrt{2x}))
derivative sin^4(6x^2)	derivative\:\sin^{4}(6x^{2})
integral de 11x^{4/7}+8x^{-6/7}	\int\:11x^{\frac{4}{7}}+8x^{-\frac{6}{7}}dx
integral de (sec(θ))/(cos(θ)-sec(θ))	\int\:\frac{\sec(θ)}{\cos(θ)-\sec(θ)}dθ
(dy)/(dx)=1-y^2	\frac{dy}{dx}=1-y^{2}
integral de e^x-1/x+4+5x^3	\int\:e^{x}-\frac{1}{x}+4+5x^{3}dx
integral de (v^2)/(sqrt(-v^2+3))	\int\:\frac{v^{2}}{\sqrt{-v^{2}+3}}dv
integral de sin(3x+4)	\int\:\sin(3x+4)dx
derivada de 2/((x-3t^2+1))	\frac{d}{dx}(\frac{2}{(x-3t)^{2}+1})
límite cuando x tiende a 1 de x(x-2)	\lim\:_{x\to\:1}(x(x-2))
límite cuando x tiende a 0+de x	\lim\:_{x\to\:0+}(x)
serie de n=0 a infinity de sin((npi)/7)	\sum\:_{n=0}^{\infty\:}\sin(\frac{nπ}{7})
derivada de sinh(9x)	\frac{d}{dx}(\sinh(9x))
integral de 0 a 1 de (e^x+e^{-x})^2	\int\:_{0}^{1}(e^{x}+e^{-x})^{2}dx
integral de 2cos(2x)-2	\int\:2\cos(2x)-2dx
derivada de (x-7/(x+2))	\frac{d}{dx}(\frac{x-7}{x+2})
integral de 1/(sqrt(12-4x-x^2))	\int\:\frac{1}{\sqrt{12-4x-x^{2}}}dx
área x^2-2,e^x,[-1,1]	area\:x^{2}-2,e^{x},[-1,1]
tangent ((4x^3))/((2-3x)^5)	tangent\:\frac{(4x^{3})}{(2-3x)^{5}}
integral de+sin^3(θ)cos^4(θ)	\int\:+\sin^{3}(θ)\cos^{4}(θ)dθ
derivative (x+9)/(x^3+x-2)	derivative\:\frac{x+9}{x^{3}+x-2}
integral de (24x)/((3x^2+7)^3)	\int\:\frac{24x}{(3x^{2}+7)^{3}}dx
integral de x^1cos(-5x)	\int\:x^{1}\cos(-5x)dx
xy^'+(x+1)y=x,y(ln(2))=1	xy^{\prime\:}+(x+1)y=x,y(\ln(2))=1
límite cuando x tiende a 0 de 4x+tan(2x)	\lim\:_{x\to\:0}(4x+\tan(2x))
integral de 13tan^3(x)	\int\:13\tan^{3}(x)dx
derivada de 4x-2y	\frac{d}{dx}(4x-2y)
taylor 9-10^{-10}e^{40x}	taylor\:9-10^{-10}e^{40x}
(dy)/(dx)-2xy=6x,y(0)=-7	\frac{dy}{dx}-2xy=6x,y(0)=-7
derivative f(x)=(t+1)/(t^3+t-2)	derivative\:f(x)=\frac{t+1}{t^{3}+t-2}
derivada de 7-4/(x-8+(2x)/(3x+1))	\frac{d}{dx}(7-\frac{4}{x-8}+\frac{2x}{3x+1})
integral de v	\int\:vdv
derivada de 1000(18^3-x^{1/3})	\frac{d}{dx}(1000(18^{3}-x)^{\frac{1}{3}})
límite cuando x tiende a 6+de x^2-36	\lim\:_{x\to\:6+}(x^{2}-36)
derivative 8(e^xcos(x)-e^xsin(x))	derivative\:8(e^{x}\cos(x)-e^{x}\sin(x))

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