Question

the integral of ∫{ 2x^12 + 5x^9 }dx / (x^5 +x³ +1)^22 power x plus

Answer 1

$\int \frac{2 {x}^{12} + 5 {x}^{9} }{ {( {x}^{5} + {x}^{3} + 1)}^{3} } dx$
$\int \frac{2 {x}^{12} + 5 {x}^{9} }{ {x}^{15} {( 1 + {x}^{ - 2} + {x}^{ - 5} )}^{3} } dx$
$\int \frac{2 {x}^{ - 3} + 5 {x}^{ - 6} }{ {( 1 + {x}^{ - 2} + {x}^{ - 5} )}^{3} } dx$

Now put,

$1 + {x}^{ - 2} + {x}^{ - 5} = t$
And solve.