Evaluate the integral. Check your result by differentiation.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3x^{4}dx}{(5x^5-4{)}^4}$

Step $1$

Notice that the numerator of the integrand is a constant multiple of $x^4$ and the derivative of $5x^5-4$ is also a constant multiple of $x^4.$ This suggests that the integral can be rewritten in the form ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^{n}du.$

Therefore, we let $u=$ and $du=dx$