Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises - Page 512: 40

$\frac 1 {10} arctan(\frac {2x} 5)+C$

$\int \frac 1 {25+4x^2}dx$ $a^2+25, u^2=4x^2$ $a=5, u=2x, \frac 1 2 du=dx$ $\frac 1 2 \int \frac {du}{a^2+u^2}$ $\frac 1 2 \times \frac 1 5 arctan(\frac {2x}5)+C$ $\frac 1 {10} arctan(\frac {2x} 5)+C$