Question

Evaluate. (Be sure to check by differentiating!) 8 6x dx (3+x0)* | (3+x0)86x® dx =0

Answer 1

`\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=(u^9)/(9)+C \\ by\text{ substituying u, one has} \\ \int (3+x^6)^86x^5dx=((3+x^6)^9)/(9)+C \end{gathered}`