Mathematics - Indefinite Integration Question with Solution | TestHub

$g(x)=\frac{x}{(1+7x^7{)}^{1/7}}$

$$\begin{array}{rl}\therefore I& =\int \frac{x^6}{(1+7x^7{)}^{1/7}}dx\\ & =\frac{1}{49}\int \frac{49x^6}{(1+7x^7{)}^{1/7}}dx\\ & =\frac{1}{49}\int \frac{d(1+7x^7)}{(1+7x^7{)}^{1/7}}dx\\ & =\frac{1}{42}(1+7x^7{)}^{6/7}+C\end{array}$$