Question

evaluate integral (sin^3(x)/cos(x)) dx

Answer 1

I know i have to convert sin^3(x) into sin(x) * sin^2(x) / cos(x)
let u = cosx
du= -sinx dx
dx= -sinx/du

sin^2(x) = 1-cos^2(x)
so -integral = ((1-u^2) / u) du
it looks like a ln function but I'm stuck from here.

Answer 2

(1 - u^2) / u = 1/u - u
-integral = ln(u) - u^2/2 + C

Answer 3

integral = u2/2 - ln(u) + C = cos^2(x) / 2 - ln(cos(x)) + C

Answer 4

so simple. thanks!

Answer 5

You are welcome.