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Problemas populares de Cálculo

(dy)/(dx)=y(5-y),y=6	\frac{dy}{dx}=y(5-y),y=6
(dr)/(dt)=(0.15r)/(0.5)+0.1	\frac{dr}{dt}=\frac{0.15r}{0.5}+0.1
integral de sin^2(x)cos^7(x)	\int\:\sin^{2}(x)\cos^{7}(x)dx
integral de 1 a infinity de 7e^{-7x}	\int\:_{1}^{\infty\:}7e^{-7x}dx
tangent y^2=x^3+3x^2,(1,2)	tangent\:y^{2}=x^{3}+3x^{2},(1,2)
integral de x^{11}sqrt(x^6+2)	\int\:x^{11}\sqrt{x^{6}+2}dx
integral de t/((sin(t^2))^2)	\int\:\frac{t}{(\sin(t^{2}))^{2}}dt
integral de 1 a 4 de 3-\|x-3\|	\int\:_{1}^{4}3-\left\|x-3\right\|dx
(dx)/(dt)+3t^5x^7+x/t =0	\frac{dx}{dt}+3t^{5}x^{7}+\frac{x}{t}=0
integral de ysqrt(6+4y-4y^2)	\int\:y\sqrt{6+4y-4y^{2}}dy
integral de 0 a 12 de x^2+x+2	\int\:_{0}^{12}x^{2}+x+2dx
integral de 2 a 3 de (32)/(sqrt(3-x))	\int\:_{2}^{3}\frac{32}{\sqrt{3-x}}dx
integral de ((x^3+3x+ln(2)))/(sqrt(x^3))	\int\:\frac{(x^{3}+3x+\ln(2))}{\sqrt{x^{3}}}dx
integral de 2x-1/3 y^2	\int\:2x-\frac{1}{3}y^{2}dy
x((dy)/(dx))+2y=10x^2	x(\frac{dy}{dx})+2y=10x^{2}
(\partial)/(\partial y)(x^2+y^2-5)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-5)
integral de 6/(5(4-7x)^3)	\int\:\frac{6}{5(4-7x)^{3}}dx
integral de 1/(1+t^4)	\int\:\frac{1}{1+t^{4}}dt
integral de (6e^x)/(sqrt(1-e^{2x))}	\int\:\frac{6e^{x}}{\sqrt{1-e^{2x}}}dx
integral de 8sec^6(t)	\int\:8\sec^{6}(t)dt
(\partial)/(\partial x)(3x^2-y)	\frac{\partial\:}{\partial\:x}(3x^{2}-y)
integral de 4/(x^3+4x)	\int\:\frac{4}{x^{3}+4x}dx
maclaurin (x^2+3)cos(-3x)	maclaurin\:(x^{2}+3)\cos(-3x)
límite cuando x tiende a 2pi+de xcsc(x)	\lim\:_{x\to\:2π+}(x\csc(x))
integral de 2 a 3 de (15)/(sqrt(3-x))	\int\:_{2}^{3}\frac{15}{\sqrt{3-x}}dx
integral de 6\sqrt[3]{x}	\int\:6\sqrt[3]{x}dx
área-x^2+y=1,[2,-2]	area\:-x^{2}+y=1,[2,-2]
integral de (r^2+r+1)e^r	\int\:(r^{2}+r+1)e^{r}dr
límite cuando x tiende a 1+de (x^2-8x+15)/(x-1)	\lim\:_{x\to\:1+}(\frac{x^{2}-8x+15}{x-1})
2xydx+(x^2+1)dy=3xdx	2xydx+(x^{2}+1)dy=3xdx
(\partial)/(\partial r)(e^rcos(θ))	\frac{\partial\:}{\partial\:r}(e^{r}\cos(θ))
integral de (x^2-2x+1)/(sqrt(x^2-2x+10))	\int\:\frac{x^{2}-2x+1}{\sqrt{x^{2}-2x+10}}dx
integral de (2x^2+5)(x^2-3x)	\int\:(2x^{2}+5)(x^{2}-3x)dx
integral de 1/(y^3)	\int\:\frac{1}{y^{3}}dy
(d^2)/(dx^2)((x^2+2x-6)/((x+1)^2))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}+2x-6}{(x+1)^{2}})
integral de 0 a pi/(24) de tan(8x)	\int\:_{0}^{\frac{π}{24}}\tan(8x)dx
derivative sqrt(e^{1+x^2)+3x^4}	derivative\:\sqrt{e^{1+x^{2}}+3x^{4}}
(dy)/(dx)y=sin(-1(6x+1))	\frac{dy}{dx}y=\sin(-1(6x+1))
integral de 10xsqrt(3x^2-4)	\int\:10x\sqrt{3x^{2}-4}dx
(\partial)/(\partial y)(x^2+2y^2-x^2y)	\frac{\partial\:}{\partial\:y}(x^{2}+2y^{2}-x^{2}y)
límite cuando x tiende a (7pi)/2+de sec(x)	\lim\:_{x\to\:\frac{7π}{2}+}(\sec(x))
derivada de (2x-9^4(x^2+x+1)^5)	\frac{d}{dx}((2x-9)^{4}(x^{2}+x+1)^{5})
derivada de 3ln(15x)	\frac{d}{dx}(3\ln(15x))
límite cuando x tiende a 3 de cos(pi/4 x)	\lim\:_{x\to\:3}(\cos(\frac{π}{4}x))
límite cuando x tiende a a de (4^2+4)/(x+5)	\lim\:_{x\to\:a}(\frac{4^{2}+4}{x+5})
(\partial)/(\partial z)(ye^z)	\frac{\partial\:}{\partial\:z}(ye^{z})
(dh)/(dt)=-2ksqrt(h)	\frac{dh}{dt}=-2k\sqrt{h}
partialfraction (x^2)/(x+1)	partialfraction\:\frac{x^{2}}{x+1}
d/(dA)(0.0155A^3-0.372A^2+3.95A+1.21)	\frac{d}{dA}(0.0155A^{3}-0.372A^{2}+3.95A+1.21)
derivada de 5e^x+8/(\sqrt[3]{x})	\frac{d}{dx}(5e^{x}+\frac{8}{\sqrt[3]{x}})
integral de-3 a-1 de 1/x	\int\:_{-3}^{-1}\frac{1}{x}dx
derivative x-1/x	derivative\:x-\frac{1}{x}
derivada de 6xln(x)	\frac{d}{dx}(6x\ln(x))
integral de (e(sqrt(x))/2)/(sqrt(x))	\int\:\frac{e\frac{\sqrt{x}}{2}}{\sqrt{x}}dx
derivada de (6(x-3^2)/(3x^2-9x-12))	\frac{d}{dx}(\frac{6(x-3)^{2}}{3x^{2}-9x-12})
derivada de 3^{x^2+1}	\frac{d}{dx}(3^{x^{2}+1})
integral de 3/x+1	\int\:\frac{3}{x}+1dx
tangent y=4(x-1x)4,\at x=2	tangent\:y=4(x-1x)4,\at\:x=2
derivada de sqrt((1+x/(2+x)))	\frac{d}{dx}(\sqrt{\frac{1+x}{2+x}})
integral de 4z+zsqrt(1-z^2)	\int\:4z+z\sqrt{1-z^{2}}dz
derivative-5e^x	derivative\:-5e^{x}
integral de (x^6)/((6-x^7)^2)	\int\:\frac{x^{6}}{(6-x^{7})^{2}}dx
límite cuando x tiende a 7 de \|x-7\|	\lim\:_{x\to\:7}(\left\|x-7\right\|)
derivative h(x)=sqrt(x)	derivative\:h(x)=\sqrt{x}
integral de x^n*ln(x)	\int\:x^{n}\cdot\:\ln(x)dx
tangent 2x^3+36x^2+210x+4	tangent\:2x^{3}+36x^{2}+210x+4
(\partial}{\partial x}(\frac{yz)/x)	\frac{\partial\:}{\partial\:x}(\frac{yz}{x})
integral de sin(2x)sin(2x)	\int\:\sin(2x)\sin(2x)dx
integral de sqrt(9-(x-4)^2)	\int\:\sqrt{9-(x-4)^{2}}dx
integral de ((log_{7}(x)))/x	\int\:\frac{(\log_{7}(x))}{x}dx
(\partial)/(\partial t)(c/(x+ct))	\frac{\partial\:}{\partial\:t}(\frac{c}{x+ct})
derivada de \sqrt[3]{tan(3x})	\frac{d}{dx}(\sqrt[3]{\tan(3x)})
límite cuando x tiende a-5 de (x^2-4)/(5-x)	\lim\:_{x\to\:-5}(\frac{x^{2}-4}{5-x})
integral de (x^2)/((x^2-36)^{5/2)}	\int\:\frac{x^{2}}{(x^{2}-36)^{\frac{5}{2}}}dx
integral de (tan^3(6/z))/(z^2)	\int\:\frac{\tan^{3}(\frac{6}{z})}{z^{2}}dz
integral de sqrt(3+x)(x+1)^2	\int\:\sqrt{3+x}(x+1)^{2}dx
y^{''}+2y^'-3y=t(e^{-3t}+e^{2t})	y^{\prime\:\prime\:}+2y^{\prime\:}-3y=t(e^{-3t}+e^{2t})
derivative e^{(-y^2)/2}	derivative\:e^{\frac{-y^{2}}{2}}
derivada de (x-2/2)	\frac{d}{dx}(\frac{x-2}{2})
derivada de x^5tan(x)	\frac{d}{dx}(x^{5}\tan(x))
serie de n=1 a infinity de 1/(n3^n)x^n	\sum\:_{n=1}^{\infty\:}\frac{1}{n3^{n}}x^{n}
(dy)/(dx)=e^{3x+2y}	\frac{dy}{dx}=e^{3x+2y}
t^2y^{''}+3ty^'-24y=0	t^{2}y^{\prime\:\prime\:}+3ty^{\prime\:}-24y=0
f(t)=3t^2	f(t)=3t^{2}
(\partial)/(\partial y)(2x^4y-2)	\frac{\partial\:}{\partial\:y}(2x^{4}y-2)
derivada de tan(5\sqrt[3]{pix})	\frac{d}{dx}(\tan(5\sqrt[3]{πx}))
límite cuando x tiende a 0 de (6sin(x))/x	\lim\:_{x\to\:0}(\frac{6\sin(x)}{x})
integral de 0 a 1 de 4/(x^2+1)	\int\:_{0}^{1}\frac{4}{x^{2}+1}dx
integral de ((x+1))/(x^3+x)	\int\:\frac{(x+1)}{x^{3}+x}dx
derivada de x(x^2+1^{1/2})	\frac{d}{dx}(x(x^{2}+1)^{\frac{1}{2}})
derivada de 2(x+4^{3/2})	\frac{d}{dx}(2(x+4)^{\frac{3}{2}})
derivada de 4/(5x^4+6\sqrt[3]{x^7})	\frac{d}{dx}(\frac{4}{5x^{4}}+6\sqrt[3]{x^{7}})
serie de n=1 a infinity de (1-5/n)^n	\sum\:_{n=1}^{\infty\:}(1-\frac{5}{n})^{n}
derivative 4/3 pix^3	derivative\:\frac{4}{3}πx^{3}
laplacetransformación sin(sqrt(2)t)	laplacetransform\:\sin(\sqrt{2}t)
integral de e^{sin(y)}	\int\:e^{\sin(y)}dy
integral de (t^3-1)/(2t-2)	\int\:\frac{t^{3}-1}{2t-2}dt
derivative 5x^4(3x-7)	derivative\:5x^{4}(3x-7)
integral de 4/(7x+5)	\int\:\frac{4}{7x+5}dx
(\partial)/(\partial y)(-(2x)/((y+2z)^2))	\frac{\partial\:}{\partial\:y}(-\frac{2x}{(y+2z)^{2}})

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