Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises - Page 438: 78

$\int\frac{cosx}{2+sinx}dx=ln(2+sinx)+constant$

Evaluate the integral $\int\frac{cosx}{2+sinx}dx$ Consider $2+sinx= t$ and $cosx.dx=dt$ Thus, $\int\frac{cosx}{2+sinx}dx=\int\frac{dt}{t}$ $=ln(t)+constant$ Hence, $\int\frac{cosx}{2+sinx}dx=ln(2+sinx)+constant$