Final answer:
The indefinite integral of cos^13(x) * sin(x) dx can be found by substitution, resulting in the expression -1/14 * cos^14(x) + C.
Step-by-step explanation:
To find the indefinite integral of cos13(x) * sin(x) dx, we can use the substitution method. Let us consider u = cos(x), then du = -sin(x) dx. By substituting, our integral becomes -∫ u13 du.
To integrate, we simply apply the power rule for integration: ∫ un du = ⅔ un+1 / (n+1) + C, with n ≠ -1. In our case, after integrating, we have -(⅔ cos14(x) / 14) + C, where C is the constant of integration.
Thus, the indefinite integral of cos13(x) * sin(x) dx is -⅔ cos14(x) / 14 + C.