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

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

then using integrating factor i've got to
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 is
Spoiler:
x(t)=\sqrt[3]{\frac{10}{3cos(t)+9sin(t)-13e^{3t}}}