Pembahasan Soal 1

\begin{equation*}
\begin{split}
& \int \sqrt [4]{x \: \sqrt [3] {x \sqrt {x}} }  \: dx \\\\
& \int x^{\frac 14} \:.\: x^{\frac 13 \:.\: \frac 14} \:.\: x^{\frac 12 \:.\: \frac 13 \:.\: \frac 14}  \: dx \\\\
& \int x^{\frac 14} \:.\: x^{\frac {1}{12}} \:.\: x^{\frac {1}{24}}  \: dx \\\\
& \int x^{\frac 14 + \frac {1}{12} + \frac {1}{24} }  \: dx \\\\
& \int x^{\frac {3}{8}}  \: dx \\\\
& \frac{1}{\frac {3}{8} + 1} x^{\frac {3}{8} + 1} + C \\\\
& \tfrac {8}{11} x^{1 \frac 38} + C \\\\
& \tfrac {8}{11} x \: \sqrt [4]{x \: \sqrt [3] {x \sqrt {x}} } + C
\end{split}
\end{equation*}