u substitution mistake

[pcooper]

I tried solving the following problem with u=x^(1/3)-1 and I did not get the book solution. So then I tried u=x^(1/3) and it matched the book. Why is my first attempt wrong? Thank you!

 

[pcooper]

oops, i forgot the 3 in front of the first term in the bottom line.

 

[Dr.Peterson]

I tried solving the following problem with u=x^(1/3)-1 and I did not get the book solution. So then I tried u=x^(1/3) and it matched the book. Why is my first attempt wrong? Thank you!
View attachment 26047

Write more steps!

The top attempt has an extra 3 in the first term, and otherwise looks good.
In the bottom attempt, if \(u = \sqrt[3]{x}-1\), then \(x = (u+1)^3\) so \(dx = 3(u+1)^2du\), not \(3u^2du\).

 

[pcooper]

Thank you!! Now I see my mistake. I appreciate your feedback! And yes, I should have written more steps clearer to spot the error. Note to self....

 

[Dr.Peterson]

When I run too fast, I trip.