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Problemas populares de Cálculo

5(dy)/(dt)+y=5t	5\frac{dy}{dt}+y=5t
integral de 30x^3sqrt(1+x^2)	\int\:30x^{3}\sqrt{1+x^{2}}dx
integral de (-4x^2)/(sqrt(4x-x^2))	\int\:\frac{-4x^{2}}{\sqrt{4x-x^{2}}}dx
límite cuando x tiende a 0 de x/(1+x^2)	\lim\:_{x\to\:0}(\frac{x}{1+x^{2}})
f(x)=arcsec(2x)	f(x)=\arcsec(2x)
integral de (sin(6x))^2	\int\:(\sin(6x))^{2}dx
y^'=cos(t)y(1-y/(100))	y^{\prime\:}=\cos(t)y(1-\frac{y}{100})
integral de 0 a 1 de x^2e^{4x}	\int\:_{0}^{1}x^{2}e^{4x}dx
serie de n=1 a infinity de 1/(4^n-3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{4^{n}-3^{n}}
2(2xy+4y-3)dx+(x+2)^2dy=0	2(2xy+4y-3)dx+(x+2)^{2}dy=0
integral de sin(5x)cos(3x)	\int\:\sin(5x)\cos(3x)dx
serie de n=1 a infinity de (3n)/(n^2+2)	\sum\:_{n=1}^{\infty\:}\frac{3n}{n^{2}+2}
integral de 0 a 2pi de 1	\int\:_{0}^{2π}1
integral de-infinity a 0 de 9^x	\int\:_{-\infty\:}^{0}9^{x}dx
integral de 5m(12m^3-10m)	\int\:5m(12m^{3}-10m)dm
pendiente 2x^2+10x-4/(x^2),\at x=-5	slope\:2x^{2}+10x-\frac{4}{x^{2}},\at\:x=-5
x((dy)/(dx))=y+sqrt(x^2-y^2)	x(\frac{dy}{dx})=y+\sqrt{x^{2}-y^{2}}
integral de 0 a 1 de xarcsin(x)	\int\:_{0}^{1}x\arcsin(x)dx
(\partial)/(\partial x)(3xz)	\frac{\partial\:}{\partial\:x}(3xz)
integral de (8e^x)/(e^{2x)-16}	\int\:\frac{8e^{x}}{e^{2x}-16}dx
integral de 0 a pi/2 de sin(2θ)	\int\:_{0}^{\frac{π}{2}}\sin(2θ)dθ
derivada de 3ln(sec(x+tan(x)))	\frac{d}{dx}(3\ln(\sec(x)+\tan(x)))
y^'-e^{x+1}=0	y^{\prime\:}-e^{x+1}=0
integral de sec(x/4)	\int\:\sec(\frac{x}{4})dx
y^{''}+9y=2sin(x)+cos(x)	y^{\prime\:\prime\:}+9y=2\sin(x)+\cos(x)
(dy)/(dx)-xy=x	\frac{dy}{dx}-xy=x
25y^{''}+90y^'+81y=0	25y^{\prime\:\prime\:}+90y^{\prime\:}+81y=0
derivada de 656112^{sqrt(x)}	\frac{d}{dx}(656112^{\sqrt{x}})
integral de 1/(sin(2x))	\int\:\frac{1}{\sin(2x)}dx
derivada de 3sec(8x)	\frac{d}{dx}(3\sec(8x))
derivative 9excos(x)	derivative\:9ex\cos(x)
integral de (x^4)/(5x^5+4)	\int\:\frac{x^{4}}{5x^{5}+4}dx
derivada de 2e^{2e^x+x}	\frac{d}{dx}(2e^{2e^{x}+x})
integral de 1/(x^2sqrt(x^2-11))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-11}}dx
derivada de e^{(ln(x)/x})	\frac{d}{dx}(e^{\frac{\ln(x)}{x}})
(dy)/(dx)=e^{9x-8y}	\frac{dy}{dx}=e^{9x-8y}
dy+0.15(y-30)dx=0	dy+0.15(y-30)dx=0
derivative 1/3 x^3-2x^2+3x-4	derivative\:\frac{1}{3}x^{3}-2x^{2}+3x-4
límite cuando x tiende a infinity de 1+8/x	\lim\:_{x\to\:\infty\:}(1+\frac{8}{x})
derivative 8x^2e^x	derivative\:8x^{2}e^{x}
derivada de sqrt(1-121x^2)arccos(11x)	\frac{d}{dx}(\sqrt{1-121x^{2}}\arccos(11x))
inversalaplace s/(s^2+64)	inverselaplace\:\frac{s}{s^{2}+64}
integral de (x^3-4x-6)	\int\:(x^{3}-4x-6)dx
derivada de (3x^2+2(2x-3))	\frac{d}{dx}((3x^{2}+2)(2x-3))
integral de (7x^2)/((9+x^2)^2)	\int\:\frac{7x^{2}}{(9+x^{2})^{2}}dx
integral de 0 a 1 de 16sin^4(x)	\int\:_{0}^{1}16\sin^{4}(x)dx
límite cuando x tiende a 3 de (x-3)/((x-3))	\lim\:_{x\to\:3}(\frac{x-3}{(x-3)})
y^{''}-2y^'+10y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=0
derivada de e^{4/x}	\frac{d}{dx}(e^{\frac{4}{x}})
límite cuando x tiende a 2 de 5x-6	\lim\:_{x\to\:2}(5x-6)
derivada de (4x-8/(x-5))	\frac{d}{dx}(\frac{4x-8}{x-5})
integral de cot(4t)sqrt(1-sin^2(4t))	\int\:\cot(4t)\sqrt{1-\sin^{2}(4t)}dt
integral de (5x^2-5x+14)/((x-2)(x^2+4))	\int\:\frac{5x^{2}-5x+14}{(x-2)(x^{2}+4)}dx
límite cuando x tiende a-3 de x/(x^2-9)	\lim\:_{x\to\:-3}(\frac{x}{x^{2}-9})
integral de 1/2 xe^{2x}	\int\:\frac{1}{2}xe^{2x}dx
derivada de 7^{x^4}	\frac{d}{dx}(7^{x^{4}})
integral de 3cos(x)y+5x^4z^2	\int\:3\cos(x)y+5x^{4}z^{2}dx
integral de e^{x+sin(y)}cos(y)	\int\:e^{x+\sin(y)}\cos(y)dy
derivada de x^2-4x-5	\frac{d}{dx}(x^{2}-4x-5)
serie de n=1 a infinity de 1/(n*(n+1))	\sum\:_{n=1}^{\infty\:}\frac{1}{n\cdot\:(n+1)}
integral de (1+sqrt(x))/(-xsqrt(x))	\int\:\frac{1+\sqrt{x}}{-x\sqrt{x}}dx
integral de 0 a 1 de-(x^2-x)	\int\:_{0}^{1}-(x^{2}-x)dx
límite cuando x tiende a 3 de-sqrt(7-x)	\lim\:_{x\to\:3}(-\sqrt{7-x})
integral de xe^{2x}	\int\:xe^{2x}dx
y^{''''}-4y^{''}=0	y^{\prime\:\prime\:\prime\:\prime\:}-4y^{\prime\:\prime\:}=0
derivada de-(2x^2/(3y^2))	\frac{d}{dx}(-\frac{2x^{2}}{3y^{2}})
integral de-9sin(sqrt(x))	\int\:-9\sin(\sqrt{x})dx
derivative f(x)=sqrt(x+\sqrt{x)}	derivative\:f(x)=\sqrt{x+\sqrt{x}}
integral de 1/(x-2x^{3/4)-8sqrt(x)}	\int\:\frac{1}{x-2x^{\frac{3}{4}}-8\sqrt{x}}dx
serie de n=0 a infinity de (5+n)/(10^n)	\sum\:_{n=0}^{\infty\:}\frac{5+n}{10^{n}}
integral de ((csc(x)+cot(x))/(sin(x)))	\int\:(\frac{\csc(x)+\cot(x)}{\sin(x)})dx
integral de x^{4035}e^{x^{2018}}	\int\:x^{4035}e^{x^{2018}}dx
límite cuando x tiende a 1 de xarcsin(x/2)	\lim\:_{x\to\:1}(x\arcsin(\frac{x}{2}))
derivada de 3*10^{2x}	\frac{d}{dx}(3\cdot\:10^{2x})
integral de tln(t+1)	\int\:t\ln(t+1)dt
(\partial)/(\partial x)(2(1+y)x)	\frac{\partial\:}{\partial\:x}(2(1+y)x)
derivative y=3^{x^2+3x}	derivative\:y=3^{x^{2}+3x}
d/(dy)((y^3)/(27)+9/(4y))	\frac{d}{dy}(\frac{y^{3}}{27}+\frac{9}{4y})
derivative sin(4x)+sin^2(4x)	derivative\:\sin(4x)+\sin^{2}(4x)
f(x)=-3log_{10}(x)	f(x)=-3\log_{10}(x)
f(x)=-2sqrt(x)	f(x)=-2\sqrt{x}
f^'(x)=5x^2+7	f^{\prime\:}(x)=5x^{2}+7
tangent 4sec(x)-8cos(x)	tangent\:4\sec(x)-8\cos(x)
integral de (sqrt(16x^2+25))/(x^4)	\int\:\frac{\sqrt{16x^{2}+25}}{x^{4}}dx
integral de 0 a pi de cos(2θ)	\int\:_{0}^{π}\cos(2θ)dθ
integral de 0 a 2 de 4x^3-3x^2+2x	\int\:_{0}^{2}4x^{3}-3x^{2}+2xdx
inversalaplace ((3s+5))/((s-5)(s+2))	inverselaplace\:\frac{(3s+5)}{(s-5)(s+2)}
integral de (4x)/(sqrt(x^2+9))	\int\:\frac{4x}{\sqrt{x^{2}+9}}dx
derivada de (x^3+1e^x)	\frac{d}{dx}((x^{3}+1)e^{x})
taylor 1/(2x+2)	taylor\:\frac{1}{2x+2}
derivada de (ln(7x)/(7x))	\frac{d}{dx}(\frac{\ln(7x)}{7x})
integral de 0 a infinity de e^{-x}x^2	\int\:_{0}^{\infty\:}e^{-x}x^{2}dx
y^'=0.0016y(2800-y)	y^{\prime\:}=0.0016y(2800-y)
integral de ((x-5))/(x^2-18x+82)	\int\:\frac{(x-5)}{x^{2}-18x+82}dx
derivative f(x)=1.5x^2+2x^{1.5}	derivative\:f(x)=1.5x^{2}+2x^{1.5}
serie de n=1 a infinity de 1/(n^4+n^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{4}+n^{2}}
derivada de (x^2-3x-4/(x+1))	\frac{d}{dx}(\frac{x^{2}-3x-4}{x+1})
límite cuando x tiende a infinity de 3/(2x)	\lim\:_{x\to\:\infty\:}(\frac{3}{2x})
derivada de sqrt(ax)+a/(sqrt(ax))	\frac{d}{dx}(\sqrt{ax}+\frac{a}{\sqrt{ax}})
derivada de 44(2x^3-5^{6/5})	\frac{d}{dx}(44(2x^{3}-5)^{\frac{6}{5}})

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