Sr Examen
Integral de arctg^3+x/(1+x)^2 dx
Solución
Ha introducido
[src]
oo / | | / 3 x \ | |atan (x) + --------| dx | | 2| | \ (1 + x) / | / 1
$$\int\limits_{1}^{\infty} \left(\frac{x}{\left(x + 1\right)^{2}} + \operatorname{atan}^{3}{\left(x \right)}\right)\, dx$$
Integral(atan(x)^3 + x/(1 + x)^2, (x, 1, oo))
Respuesta (Indefinida)
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/ / | | | / 3 x \ 1 | 3 | |atan (x) + --------| dx = C + ----- + | atan (x) dx + log(1 + x) | | 2| 1 + x | | \ (1 + x) / / | /
$$\int \left(\frac{x}{\left(x + 1\right)^{2}} + \operatorname{atan}^{3}{\left(x \right)}\right)\, dx = C + \log{\left(x + 1 \right)} + \int \operatorname{atan}^{3}{\left(x \right)}\, dx + \frac{1}{x + 1}$$
Respuesta
[src]
oo / | | 3 2 3 3 | x + atan (x) + x *atan (x) + 2*x*atan (x) | ----------------------------------------- dx | 2 | (1 + x) | / 1
$$\int\limits_{1}^{\infty} \frac{x^{2} \operatorname{atan}^{3}{\left(x \right)} + 2 x \operatorname{atan}^{3}{\left(x \right)} + x + \operatorname{atan}^{3}{\left(x \right)}}{\left(x + 1\right)^{2}}\, dx$$
=
=
oo / | | 3 2 3 3 | x + atan (x) + x *atan (x) + 2*x*atan (x) | ----------------------------------------- dx | 2 | (1 + x) | / 1
$$\int\limits_{1}^{\infty} \frac{x^{2} \operatorname{atan}^{3}{\left(x \right)} + 2 x \operatorname{atan}^{3}{\left(x \right)} + x + \operatorname{atan}^{3}{\left(x \right)}}{\left(x + 1\right)^{2}}\, dx$$
Integral((x + atan(x)^3 + x^2*atan(x)^3 + 2*x*atan(x)^3)/(1 + x)^2, (x, 1, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.