Integration by substitution

[mikewill54]

Hi working through the following example, just wondering if anyone knows why they’ve split the u’s

 

[AvgStudent]

Hi working through the following example, just wondering if anyone knows why they’ve split the u’s
View attachment 31605

[math]u^{\frac{4}{3}}=u^{1+\frac{1}{3}}=u\cdot u^{\frac{1}{3}}=u\cdot \sqrt[3]{u}[/math]and I think it's more for "aesthetic" reasons

 

[Steven G]

Personally I would not have split the u's. However, they could since it is allowable.

 

[mikewill54]

Thought it was something just aesthetic
Thanks

 

[Dr.Peterson]

Hi working through the following example, just wondering if anyone knows why they’ve split the u’s
View attachment 31605

It would be perfectly legal to leave it as [imath]u^{\frac{4}{3}}[/imath]; but they evidently have a habit of writing such expressions in radical form. and it is appropriate in that case to simplify the radical (minimizing what is in the radicand).