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

$\displaystyle \frac{dx}{dt}+x=x^4sin(t)$ it is given that x(0)=-1

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

$\displaystyle \frac{dy}{dt}-3y=-3sin(t)$

then using integrating factor i've got to

$\displaystyle ye^{-3t}=\int{3e^{-3t}.sin(t)} dt$

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: