Question

integrate dx/9+4x^2

Answer 1

\[\int\limits_{}^{} 9 +4x^2 dx\]
Is this what you mean?

Answer 2

First split it up into two integrals added together.

Answer 3

i think
9+4x^2 is in the denominator

if so
try
x= (3/2) tan u

Answer 4

\[\int \frac{dx}{9+4x^2}\]
Take 4 common from the denominator to make things easier.
\[\frac{1}{4} \int \frac{dx}{\frac{9}{4} + x^2}\]
It is helpful here to know that, \[\int \frac{dx}{a^2 + x^2} = \frac{1}{a} \tan^{-1} (\frac{x}{a}) + C\]
Can you get the integral now? :)