1. 32(x^2+1)^7 dx

in front to the bracket is the "s" like sign at the top is 1 and at the bottom 0


thank you

32\int_{0}^{1}(x^{2}+1)^{7}dx

One way is to just expand out and integrate term by term.

(x^{2}+1)^{7}=x^{14}+7x^{12}+21x^{10}+35x^{8}+35x^ {6}+21x^{4}+7x^{2}+1

There is a lot of them, but they are easy to integrate.