Question

Solve $\int \frac{(4x^3+5x^4)}{{(x^5+x^4+6)}^2}dx$

Answer 1

We have,

$I=\int \frac{(4x^3+5x^4)}{{(x^5+x^4+6)}^2}dx$

Let $t=x^5+x^4+6$

$dt=(5x^4+4x^3)dx$

Therefore,

$I=\int \frac{1}{{\left(t\right)}^2}dt$

$I=-\frac{1}{t}+C$

On putting the value of $t$, we get

$I=-\frac{1}{(x^5+x^4+6)}+C$

Hence, this is the answer.