# U-substitution integral help

mattmannmf
determine the indef. integral:
S= integral for me

S 6/ (sqrt(x)*(x+81)) dx the (x+81) is not included within the sqrt

I am stuck. I dont think U-substitution will work and im not sure about intigration by parts. It doens't look like i can use trig substitution either. Would partial fractions work? any suggestions please

l'Hôpital

Try u^2 = x.

mattmannmf

so my du would be 1/2 x ^-1.2 ?

l'Hôpital

Yup.

mattmannmf

alright thanks, ill work it out and see what i come up with

mattmannmf

ok heres what i got:

= 6 S du/(u^2+81)... which is arc tan So

= 6* 1/9 arctan (u/9) +C
did i do the arctan right?

l'Hôpital

ok heres what i got:

= 6 S du/(u^2+81)... which is arc tan So

= 6* 1/9 arctan (u/9) +C
did i do the arctan right?

Don't forget to swap back to x, though. Otherwise, great.

mattmannmf

oh yes, thanks!

mattmannmf

so its 6 * 1/9 arctan (sqrt (x) /9) +c