# Primitive of x over x squared plus a squared/Proof 1

$\ds \int \frac {x \rd x} {x^2 + a^2} = \frac 1 2 \map \ln {x^2 + a^2} + C$
 $\ds u$ $=$ $\ds x^2 + a^2$ $\ds \leadsto \ \$ $\ds \frac {\d u} {\d x}$ $=$ $\ds 2 x$ Power Rule for Derivatives and Derivative of Constant $\ds \leadsto \ \$ $\ds \int \frac {x \rd x} {x^2 + a^2}$ $=$ $\ds \frac 1 2 \ln \size {x^2 + a^2} + C$ Primitive of Function under its Derivative $\ds$ $=$ $\ds \frac 1 2 \, \map \ln {x^2 + a^2} + C$ Absolute Value of Even Power‎
$\blacksquare$