Chapter 4 - Integrals - 4.5 The Substitution Rule - 4.5 Exercises - Page 346: 17

$\frac{tan^4\theta}{4} +C$

Evaluate the Integral using substitution: $\int sec^2(\theta )tan^3(\theta) d\theta$ Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$ $u= tan(\theta)$ $du =sec^2(\theta)$ Solve the integral in terms of $u$: $\int (u)^3du$ $\frac{u^4}{4}+C $ Substitute for $u$: $\frac{tan^4\theta}{4} +C$