Question

alguien me ayuda con esta integral con resolucion

Answer 1

Respuesta:

$-\frac{5}{27}\ln \left|x+1\right|+\frac{1}{9\left(x+1\right)}+\frac{32}{27}\ln \left|x-2\right|-\frac{5}{9\left(x-2\right)}+C$

Explicación paso a paso:

$\int \frac{x^3+x^2-2x-3}{\left(x+1\right)^2\left(x-2\right)^2}dx$

$\int \:-\frac{5}{27\left(x+1\right)}-\frac{1}{9\left(x+1\right)^2}+\frac{32}{27\left(x-2\right)}+\frac{5}{9\left(x-2\right)^2}dx$

$-\int \frac{5}{27\left(x+1\right)}dx-\int \frac{1}{9\left(x+1\right)^2}dx+\int \frac{32}{27\left(x-2\right)}dx+\int \frac{5}{9\left(x-2\right)^2}dx$

$-\frac{5}{27}\ln \left|x+1\right|-\left(-\frac{1}{9\left(x+1\right)}\right)+\frac{32}{27}\ln \left|x-2\right|-\frac{5}{9\left(x-2\right)}$

$-\frac{5}{27}\ln \left|x+1\right|+\frac{1}{9\left(x+1\right)}+\frac{32}{27}\ln \left|x-2\right|-\frac{5}{9\left(x-2\right)}$

$-\frac{5}{27}\ln \left|x+1\right|+\frac{1}{9\left(x+1\right)}+\frac{32}{27}\ln \left|x-2\right|-\frac{5}{9\left(x-2\right)}+C$

Espero haberte ayudado ;).