G
Guest
Guest
We can only use substitution. I can do all the other problems my teacher gave us but not this one.
We can only use substitution. I can do all the other problems my teacher gave us but not this one.
Take \(\displaystyle \L u=x^3+8,\) so that \(\displaystyle \L du=3x^2\,dx.\) Then:
\(\displaystyle \L\qquad\begin{eqnarray}
\int x^5(x^3+8)^{2/3}\,dx
&=&\frac13\int x^3(x^3+8)^{2/3}(3x^2\,dx)\\
&=&\frac13\int(u-8)u^{2/3}\,du\\
&=&\frac13\int(u^{5/3}-8u^{2/3})\,du
\end{eqnarray}\)
and so on.
\(\displaystyle \L\qquad\begin{eqnarray}
\int x^5(x^3+8)^{2/3}\,dx
&=&\frac13\int x^3(x^3+8)^{2/3}(3x^2\,dx)\\
&=&\frac13\int(u-8)u^{2/3}\,du\\
&=&\frac13\int(u^{5/3}-8u^{2/3})\,du
\end{eqnarray}\)
and so on.
