How to deal with multiplication inside of integral? I have an undefined integral like this:
\begin{aligned}
\ \int x^3 \cdot \sin(4+9x^4)dx
\end{aligned}
I have to integrate it and I have no idea where to start. I have basic formulas for integrating but I need to split this equation into two or to do something else.

Note that $$(4+9x^4)' = 36x^3$$
So that your integral becomes
$$\int x^3 \sin(4+9x^4)dx$$
$$\dfrac{1}{36}\int 36x^3 \sin(4+9x^4)dx$$
$$\dfrac{1}{36}\int \sin u du$$
Which you can easily solve.
