Answer
$\int\frac{sin2x}{1+cos^{2}x}dx=-ln(1+cos^{2}x)+constant$
Work Step by Step
Evaluate the integral $\int\frac{sin2x}{1+cos^{2}x}dx$
Consider $cos^{2}x=t$
and
$2cosx(-sinx)dx=dt$
This implies
$sin2xdx=-dt$
Thus, $\int\frac{sin2x}{1+cos^{2}x}dx=-\int\frac{1}{1+t}$
$=-ln|1+t|+constant$
Hence,$\int\frac{sin2x}{1+cos^{2}x}dx=-ln(1+cos^{2}x)+constant$
