How Do You Solve the Integral ∫x/(6x-x^2)^3/2 dx Using Trig Substitution?

[Oalvarez]

1. I need help solving this integral, I've tried using trig substitution, but I'm getting nowhere with it.


∫x/(6x-x^2)^3/2dx



Like I said before, I tried changing the bottom to a radical and trig substituting but it doesn't seem to get me anywhere. Thanks in advanced for any help.

 

[Simon Bridge]

Welcome to PF;
You are trying to evaluate the indefinite integral:
$$\int \frac{x}{(6x-x^2)^{3/2}}\;dx$$

Note: $(6x-x^2)^{3/2} = x^{3/2}(6-x)^{3/2}$ ... probably won't help a lot: try again but complete the square first.

 

[vela]

←

1. I need help solving this integral, I've tried using trig substitution, but I'm getting nowhere with it.


∫x/(6x-x^2)^3/2dx



Like I said before, I tried changing the bottom to a radical and trig substituting but it doesn't seem to get me anywhere. Thanks in advanced for any help.

Please show your work.