cau 20

db=\(\int\limits^x_{\frac{1}{e}}\left(1+lnt\right)dlnt=\left(lnt+\frac{1}{2}ln^2t\right)|^x_{\frac{1}{e}}=\left(lnx+\frac{1}{2}ln^2x\right)+\frac{1}{2}=18\Leftrightarrow\xrightarrow[lnx=-7\left(L\right)]{lnx=5\Leftrightarrow x=e^5}\)

cau 13

\(\int_0^{\frac{\Pi}{6}}\sin^nx.cosxdx=\int_0^{\frac{\Pi}{6}}sin^nxdsinx=\left(\frac{1}{n+1}\sin^{n+1}x\right)|^{\frac{\Pi}{6}}_0=\frac{1}{n+1}.\frac{1}{2^{n+1}}=\frac{1}{64}\Rightarrow n=3\)