Question

intergral 9/1+9x^2

Answer 1

\[\Large \int\limits \frac{9}{1+9x^2}dx\]Looks very similar to arctan yes?\[\Large \int\limits \frac{1}{1+x^2}dx \quad=\quad \arctan x\]

Answer 2

Umm have you learned how to do trig subs?

Answer 3

Oh I guess we don't need a trig sub here :) lol.
Let's just make a u-sub.

Answer 4

\[\Large \int\limits \frac{9}{1+9x^2}dx\quad=\quad 3\int\limits\frac{1}{1+(3x)^2}(3dx)\]
\[\Large u=3x \qquad\to\qquad du=3dx\]

Answer 5

\[\Large = \quad 3\int\limits \frac{1}{1+(u)^2}(du)\]

Answer 6

See how we can relate it back to the arctan integral? :o