Question

Evaluate this integral.

Answer 1

\[\int\limits_{?}^{?} \frac{ 1 }{ 9 + x ^{2} } dx\]

Answer 2

looks almost like the derivative of arctangent
make it look more like it

Answer 3

arc tangent is \[\int\limits_{?}^{?} \frac{ 1 }{ 1+u ^{2} }dx\]

do we do let u = 9 + x^2 ?

Answer 4

rewrite \(\frac{1}{9+x^2}\) as \[\frac{1}{9}\times \frac{1}{1+(\frac{x}{3})^2}\]

Answer 5

you get
\[\frac{1}{9}\int \frac{dx}{1+\left(\frac{x}{3}\right)^2}\] and then a simple mental u -sub \(u=\frac{x}{3}\) give you arctan right away

Answer 6

let me try this.. thanks

Answer 7

yw