u substitution with indefinite integrals

[Dorian Gray]

Greetings Mathematicians,


I am having issues with the step involving the dx part. I attached a copy of my work. I am not sure how I am supposed to incorporate my du into the problem.... Thank you for any help, comments, and suggestions.

 

[pka]

Greetings Mathematicians,


I am having issues with the step involving the dx part. I attached a copy of my work. I am not sure how I am supposed to incorporate my du into the problem.... Thank you for any help, comments, and suggestions.View attachment 1900

\(\displaystyle \displaystyle\int {\frac{x}{{\sqrt[4]{{x + 2}}}}dx = \int {\frac{{u - 2}}{{\sqrt[4]{u}}}du = \int {\left( {{u^{\frac{3}{4}}} - {2u^{\frac{-1}{4}}}} \right)} } } du\)

 

[Dorian Gray]

thank you

Thank you very much pka for your answer. It is greatly appreciated!

 

[HallsofIvy]

Since pka has corrected what he wrote, this is no longer necessary.

 

[Dorian Gray]

thanks!

Thank you for your help pka and HallsofIvy. I see how the u and the x were manipulated to get what was needed for the problem