Book:Christopher Clapham/The Concise Oxford Dictionary of Mathematics/Sixth Edition/Errata

Errata for 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.)

Reduction Formula for $\ds \int \sin^n x \rd x$

Appendix $8$: Integrals: Reduction Formulae

For $I_n = \int \sin^n x \rd x$, where $n \ge 2$, then

$I_n = -\dfrac {\sin^n x \cos x} n + \dfrac {n - 1} n I_{n - 2}$.

Reduction Formula for $\ds \int \sin^n x \rd x$

Appendix $8$: Integrals: Reduction Formulae

For $I_n = \int \cos^n x \rd x$, where $n \ge 2$, then

$I_n = \dfrac {\cos^n x \sin x} n + \dfrac {n - 1} n I_{n - 2}$.