Can Partial Fractions Help Solve This Tricky Indefinite Integral?

[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 don't think U-substitution will work and I am 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 here's 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 here's 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