Question

Evaluate the indefinite integral of:
Sin 2x / 1 + cos^(2)(x) * dx

Answer 1

If you let:
\(u = cos(x)\\du = -sin(u) \\ dx = \frac{-du}{sin(x)}\)

Then the integral becomes:
\[\int -\frac{1}{u^2 + 1} du\]

Answer 2

Which \[\frac{1}{u^2 + 1} = \tan^{-1}(u) = \tan^{-1}(\cos(x))\]