Got this questions that I'm struggling with and need help finding the solution to the following differential equation

it is given that x(0)=-1

I used bernoulli method to change it into a differential equation and got

then using integrating factor i've got to

from here I need help with this cyclic integral thingy :eek3:

tried many times to get what they got in the book as solution to no avail.

Solution isSpoiler: