Question

integrate sqrt(3x+1)/(3x+4)

Answer 1

is everything under sqrt or just the numerator ?

Answer 2

If it's the latter, I think a substitution would work.

Answer 3

just numerator. Trying sub. getting messy.

Answer 4

what substitution are you trying ?

Answer 5

u=3x, du=3dx, 1/3du then split those integrals up after the sub. then sub again for t=sqrt(u), dt=2/3u^(3/2)

Answer 6

no no

Answer 7

try \(\large u=\sqrt{3x+1}\)

Answer 8

denominator = u^2+3

Answer 9

du = .. ?

Answer 10

1/2(3x+1)^-1/2*3

Answer 11

or can i say ,
du = 3/ (2u) dx
?

Answer 12

and substitute (2u du)/3 in place of dx

Answer 13

getting this ?

Answer 14

yeah never done or thought about it like that.

Answer 15

time to try out new things! :)
you will do this again in many problems, for sure.

Answer 16

thanks

Answer 17

oh, so will you be able to solve this now ?

Answer 18

I think so, the 3x+4 on the denominator stays though when i sub right.

Answer 19

3x+4 = 3x+1 + 3 = u^2+3
we need to get rid of every x when we substitute...

Answer 20

right just confused becasue u was sqrt(3x+1) not just 3x+1

Answer 21

yeah..