00:01
Evaluate this integral first.
00:01
We want to rewrite it as the integral of 2 and then times tangent squared of 9x times tangent cubed of 9x, dx.
00:18
Then tangent squared is second squared of 9x minus 1, so that'll be integral of 2, secan squared of 9x minus 1, times tangent cubed of 9x dx.
00:32
It's the same as the integral of 2, 2 2 2 squared of 9x times tangent cubed of 9x dx minus the integral of 2 tangent cubed of 9x dx dx minus the integral of 2 tangent cubed of 9x dx.
00:53
Now we can apply substitution in here, let's say u equals, tangent of 9x, then du would be 9 secan squared of 9x dx, or 1 over 9, du equals sequins squared of 9x dx.
01:13
And then this can be rewritten as tangent squared of 9x times tangent of 9x, but tangent squared is also secan squared of 9x minus 1.
01:27
So then from here we should have integral of 2 u to the 3rd times 1 over 9 d u minus the integral of 2 times 2x squared of 9x minus 1 times tangent of 9x d x...