Answer
$\frac{sec(3t)}{3} +C$
Work Step by Step
Evaluate the Integral using substitution: $\int sec(3t)tan(3t)dt$
Substitution Rule: $\int f(g(x))gā(x)dx = \int f(u)du$
$u= 3t$
$du =3$
Since $du$ in the expression is equal to $1$ it must be multiplied by $\frac{1}{3}
$
Solve the integral in terms of $u$:
$\int sec(u)tan(u)(\frac{1}{3})du$
$\frac{1}{3}\int sec(u)tan(u)du $
$\frac{1}{3}sec(u) +C$
$\frac{sec(u)}{3} + C$
Substitute for $u$:
$\frac{sec(3t)}{3} +C$