How Do I Solve This Integral with Completing the Square and Long Division?

[Fiorella]

Hello, can someone help me solve this integral? I think I need to complete the square...I've tried many other things but I don't know what else to use

and

With the last one I did long division and I ended up with: x + x/ (x - 1)...so I can easily solve the first integral of X but now I can't solve the other part... :(

 

[Feldoh]

Try using latex, it might be a while before we can view your image.

 

[Fiorella]

I posted the image differently :)

 

[Feldoh]

U-sub is the easiest on the first one, u-sub and factor actually...

U-sub the second one too

 

[olgranpappy]

Hello, can someone help me solve this integral? I think I need to complete the square...I've tried many other things but I don't know what else to use

and

With the last one I did long division and I ended up with: x + x/ (x - 1)...so I can easily solve the first integral of X but now I can't solve the other part... :(

you could rewrite

\frac{x}{(x-1)}

as

1+\frac{1}{x-1}

if that is any easier for you.

 

[HallsofIvy]

Hello, can someone help me solve this integral? I think I need to complete the square...I've tried many other things but I don't know what else to use

Not "complete the square", the denominator is a cube, not a square! The substitution
u= -x³+ 9x+ 1 works nicely.

and

With the last one I did long division and I ended up with: x + x/ (x - 1)...so I can easily solve the first integral of X but now I can't solve the other part... :(

You need to review your long division! x² divided by x- 1 is x+ 1+ 1/(x-1).

 

[Fiorella]

Thank you so much everybody :)