Primitive of Reciprocal of x squared plus a squared/Examples/16 + x^2

Example of Use of Primitive of $\dfrac 1 {x^2 + a^2}$

$\ds \int \dfrac 1 {16 + x^2} \rd x = \dfrac 1 4 \arctan \dfrac x 4 + C$

Proof

From Primitive of $\dfrac 1 {x^2 + a^2}$:

$\ds \int \frac {\d x} {x^2 + a^2} = \frac 1 a \arctan \frac x a + C$

The result follows by setting $a = 4$.

$\blacksquare$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Exercises $\text {XIV}$: $13$.