Question

how do i integrate this

3/x + (x + 1) / (x^2 + 8)

u= x^2+8?
du=2x?

Answer 1

Write it as
\[
\frac 3 x+ \frac x {x^2+8} + \frac 1 {x^2+8}
\]
The first two integrals involves natural logairthm in the last one involves
\[\tan^{-1}
\]
For the last integral, I suggest you use substitution with
\[
x =\sqrt 8 \tan(u)
\]

Answer 2

hm, so u=sqrt of 8 tan (u)
du=

Answer 3

\[ dx = \sqrt 8 \sec^2(u) du

\]