1. ## Definite integral

help with finding the definite integral using u substitution.
({sec^2[1/x^37]}/x)dx. U=(1/x^37)

And

x^3(2 + x^4)^6 dx. U =(2 + x^4).

2. Originally Posted by doneng

x^3(2 + x^4)^6 dx. U =(2 + x^4).
Your first one does not make sense so I do this one.
If $u=2+x^4$ then $(2+x^4)^6 = u^6$ and $u'=4x^3$.

Thus we will write, $\int (2+x^4)^6x^3 dx = \frac{1}{4}\int \underbrace{(2x+x^4)^6}_{u^6}\underbrace{[4x^3]}_{u'} dx = \frac{1}{4}\int u^6 du$

This integral is, $\frac{1}{28}u^7 + C = \frac{1}{24}(2+x^4)^7 + C$.