Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §7.2 Trigonometric Integrals, #21 · Calculus · Techniques of integration

(a) Separate … from … and integrate … by parts

(a) Separate $d v = sin x d x$ from $u = sin^{n - 1} x$ and integrate $\int sin^{n} x d x$ by parts.
(b) Substitute $1 - sin^{2} x$ for $cos^{2} x$ to find a reduction formula like equation (7).

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §7.2 Trigonometric Integrals, #21

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