1. ## Integration by substitution

Hi there. I'm new here :-)

I've been going through a fair few substitution questions, but I have been stumped on this one.

I have to solve the following by substitution:
$
\int \sqrt{x^3+1} * x^5 dx$

Now normally I find these questions relatively easy, where all the values under the square root are substituted for u.

This question does not seem to work the same way since $du = 3x^2 dx$ or $x^2=du/3$

Clearly this will not replace the $x^5$ term outside the square root.

Any ideas? :-)

2. Originally Posted by fityfity
Hi there. I'm new here :-)

I've been going through a fair few substitution questions, but I have been stumped on this one.

I have to solve the following by substitution:
$
\int \sqrt{x^3+1} * x^5 dx$

Now normally I find these questions relatively easy, where all the values under the square root are substituted for u.
Yes, exactly right. Let $u= x^3+ 1$

This question does not seem to work the same way since $du = 3x^2 dx$ or $x^2=du/3$
Yes, and $x^5dx= x^3(x^2dx)= (u- 1)du/3$.

Clearly this will not replace the $x^5$ term outside the square root.

Any ideas? :-)

3. Ahh that makes so much sense

It always appears easy once someone shows you

Thank you very much for your help