Answer :
[tex]\begin{gathered} \int (3+x^6)^86x^5dx \\ \text{let u be} \\ u=3+x^6\Rightarrow du=6x^5dx \\ \text{hence} \\ \int (3+x^6)^86x^5dx\Rightarrow\int (u^{})^8du \\ \text{therefore} \\ \int (u^{})^8du=\frac{u^9}{9}+C \\ by\text{ substituying u, one has} \\ \int (3+x^6)^86x^5dx=\frac{(3+x^6)^9}{9}+C \end{gathered}[/tex]