Integral of x^2(3x^3+4)^4
and (x^4)/(3x^5+2)
Thanks! =)
here is the first, the second one is done similarly. as for the way we plug in our substitution, some people do it differently. this is the way i like to do it. tell me if you get it
Let
So our integral becomes:
so as you see. i wrote the 1/9 du instead of x^2 dx, i then replaced what was in the brackets by u, as my substitution demands.
Back-substitute:
what you did is what u-substitution imitates. it is more or less the formalization of your method. some students cannot see that however, so substitution is best for beginners i think. but yes, you are correct, that is a valid way to do the problem, and a way Krizalid may have suggested