Question

evaluate the integral

(integral sign) cos x dx/ 1+8 sinx

Answer 1

Use U-Substitution. Let u = 1+8sinx.

Answer 2

can u explain how to do it please.

Answer 3

let t=1+8sin(x)
then
dt=8cos(x)dx
1/8dt=cos(x)dx
integral becomes
\[\Large \frac{1}{8}\int\limits_{}^{} \frac{1}{t}dt\]
you may know that formula that
\[\Large \int\limits_{}^{} \frac{1}{x}dx =\ln(x)+C\]
use this to evaluate hte above integral then substitute back t=1+8sin(x)