Question

How do you do this question?

Answer 1

Explanation:

∫ 15 ln(x) dx / (x √(6 + (ln(x))²))

Substitute: If u = ln(x), then du = 1/x dx.

∫ 15 u du / √(6 + u²)

Substitute again: If v = 6 + u², then dv = 2u du.

∫ 15/2 dv / √v

15/2 ∫ v^-½ dv

15 v^½ + C

15√v + C

15√(6 + u²) + C

15√(6 + (ln(x))²) + C