Question

Indefinite integral:

Answer 1

http://prntscr.com/3eh9rs

Answer 2

\[\int\frac{4+9x}{1+x^2}~dx=4\int\frac{dx}{1+x^2}+\frac{9}{2}\int\frac{2x}{1+x^2}~dx\]
Trig sub for the first integral, if you're not familiar with the formula for \(\arctan x\). THe second can use an simpler sub, \(u=1+x^2\).

Answer 3

This can also be written as
\[\int\limits \frac{ 4 }{ 1+x^2} + \int\limits \frac{ 9x }{1+x^2 }\]

Answer 4

Yeah same as @SithsAndGiggles