# Thread: Indefinite intergral

1. ## Indefinite intergral

Hello all =],
"The indefinite integral $\int (5x-4)^4 dx$ is equal to:"

Could anyone explain what happens here and the steps that i need to go through. I understand some of the steps but not all of them.

According to my text book the answer is;

$
\frac{1}{25} (5x-4)^5 + c
$

Thanks

2. Hello,

the book wants you to evaluate the indefinite integral, $\int (5x-4)^4~dx$.

There may be a few ways to deal with this. We can expand (5x-4)^4 using binomial theorem, then integrate it term by term. But this is long, tiring and unnecessary, so we won't use this approach.

If we can reduce 5x-4 to one term, we can integrate it easily.

Substitute $u=5x-4$ and it's easy to finish from there.

3. Thanks mate!