indefinite integral substitution trickery

Question

I want to find the indefinite integral using substitution on the above. I needed a few sets of eyes and also maybe the appropriate dunce cap if need be. I am wondering if I am on the right track, or if I am missing crucial steps and or points to making the solution explanatory? They don't call me captain confused for nothing. Here is the work that I have completed for this problem...

Answer 1

$$ \int( x^2 + 5)^4\Big( 2x\,dx\Big) - 5 \int (x^2-5)^4\,dx $$ The first integral becomes $$ \int u^5 \, du. $$ The second integral could be treated simply by expanding $(x^2-5)^4$, but that would be inconvenient if we had $(x^2-5)^{40}$. My first thought for that is $(\sqrt{5}\sec\theta)^2 - 5)^{40} = (\tan^2\theta)^{40}$, and then $dx = \sqrt{5} \sec\theta\tan\theta\,d\theta$. etc.