QuestionUse a suitable change of variables to determine the indefinite integral. $$\int\left(1-\cos ^{4}(x)\right)^{5} \cos ^{3}(x) \sin (x) d x=\square+C$$
Question Help: VIDEO Submit Question

Studdy Solution
Integrate the simplified expression:
$$-\frac{1}{4} \int v^5 \, dv$$
$$= -\frac{1}{4} \cdot \frac{v^6}{6} + C$$
$$= -\frac{1}{24} v^6 + C$$
Substitute back to the original variable:
$$v = 1 - \cos^4(x)$$
$$= -\frac{1}{24} (1 - \cos^4(x))^6 + C$$
The indefinite integral is:
$$\boxed{-\frac{1}{24} (1 - \cos^4(x))^6 + C}$$