Don't know how to work out the following integral.
Substituting cos x^5 = t does not seem to work.
This looks much harder than it is.
Let
Another way of solving for "du" is . But we don't want just x^4dx, we want 2x^4, so multiply by 2 on both sides to get . Now we're getting somewhere.
So plug everything back in. Our new integral in terms of u is...
Now what's ?? .
See it now?
One thing I hate about integral is checking differenciability intervals and domains. Since I am lazy here was my approach.
Express as,
Now,
Thus,
Let,
Thus,
Where,
is an anti-derivative of
So the problem reduces to finding,
Which should be doable by integration by parts.