U-substitution integral help

  • Thread starter mattmannmf
  • Start date
  • #1
mattmannmf
172
0
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
 

Answers and Replies

  • #2
l'Hôpital
258
0


Try u^2 = x.
 
  • #3
mattmannmf
172
0


so my du would be 1/2 x ^-1.2 ?
 
  • #4
l'Hôpital
258
0


Yup.
 
  • #5
mattmannmf
172
0


alright thanks, ill work it out and see what i come up with
 
  • #6
mattmannmf
172
0


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?
 
  • #7
l'Hôpital
258
0


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.
 
  • #8
mattmannmf
172
0


oh yes, thanks!
 
  • #9
mattmannmf
172
0


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

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