Answer
$\frac{tan(2\theta)}{2} +C$
Work Step by Step
Evaluate the Integral using substitution: $\int sec^2(2\theta)d\theta$
Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$
$u= 2\theta$
$du =2$
Since $du$ in the expression is equal to $1$ it must be multiplied by $\frac{1}{2}
$
Solve the integral in terms of $u$:
$\int sec^2(u)(\frac12)du$
$\frac{1}{2}\int sec^2(u)du $
$\frac{1}{2}tan(u) +C$
$\frac{tan(u)}{2} + C$
Substitute for $u$:
$\frac{tan(2\theta)}{2} +C$
