Question

Find the integral using substitution:
(2+ ln x)^1/2/(x)

Answer 1

let u = (2+ln x)

Answer 2

\(\large \frac{(2+ ln x)^{\frac{1}{2}}}{x}\)

Answer 3

like that ?

Answer 4

What is du?

Answer 5

Yes, ganeshie8, just like that.

Answer 6

du= 1/x?

Answer 7

since we can deal wid ENTIRE thing inside radical at a time,
simply sub whatever inside radical as u

Answer 8

yes...so what form does the integral have?

Answer 9

"dx" if that is what you are looking for.

Answer 10

If u = (2+lnx), then du = dx/x...agree?

Answer 11

dx/x = (1/x) dx

Answer 12

Yes

Answer 13

So the entire integrand called (2 + ln x)^(1/2) dx/x transforms into the form u^(1/2) du....agree?

Answer 14

because u = 2+ln x and everything else is just du, so you have u^1/2 du

Answer 15

Yes i got to that step and then I got confused and did not know what to do.

Answer 16

the integral of u^(1/2) du is just u^(3/2)/(2/3) = 2/3 (u^(3/2) + C

Now just substitute (2+ln x) for u

Answer 17

Oh, I think I over complicated it when I was trying to work through it. Thank you Easyaspi314.

Answer 18

welcome.