Chapter 4 - Integrals - 4.5 The Substitution Rule - 4.5 Exercises - Page 346: 26

$-\frac{1}{tanx} +C$

Evaluate the Integral using substitution: $\int \frac{sec^2x}{tan^2x}dx$ Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$ $u= tan(x)$ $du =sec^2(x)$ Solve the integral in terms of $u$: $\int \frac{1}{u^2}du$ $-\frac{1}{u} +C$ Substitute for $u$: $-\frac{1}{tanx} +C$ Which can also be written as: $-cotx +C$