QuestionConsider the indefinite integral $\int x^{5} \cdot \sqrt[5]{x^{6}-6} d x$ : This can be transformed into a basic integral by letting $u=$ $\square$ and $$d u=\square d x$$
Performing the substitution yields the integral $\square$ $d u$

Studdy Solution
Simplify and solve the integral:
The integral becomes:
$$\frac{1}{6} \int u^{1/5} \, du$$
Integrate:
$$\frac{1}{6} \cdot \frac{u^{1/5 + 1}}{1/5 + 1} + C$$
$$= \frac{1}{6} \cdot \frac{u^{6/5}}{6/5} + C$$
$$= \frac{5}{36} u^{6/5} + C$$
Substitute back $u = x^6 - 6$:
$$= \frac{5}{36} (x^6 - 6)^{6/5} + C$$
The solution to the integral is:
$$\boxed{\frac{5}{36} (x^6 - 6)^{6/5} + C}$$