Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 14/Integrals Involving Sine of a x and Cosine of a x

Integrals Involving $\sin a x$ and $\cos a x$

$14.399$: Primitive of $\sin a x \cos a x$

$14.400$: Primitive of $\sin p x \cos q x$

$14.401$: Primitive of $\sin^n a x \cos a x$

$14.402$: Primitive of $\cos^n a x \sin a x$

$14.403$: Primitive of $\sin^2 a x \cos^2 a x$

$14.404$: Primitive of $\dfrac 1 {\sin a x \cos a x}$

$14.405$: Primitive of $\dfrac 1 {\sin^2 a x \cos a x}$

$14.406$: Primitive of $\dfrac 1 {\sin a x \cos^2 a x}$

$14.407$: Primitive of $\dfrac 1 {\sin^2 a x \cos^2 a x}$

$14.408$: Primitive of $\dfrac {\sin^2 a x} {\cos a x}$

$14.409$: Primitive of $\dfrac {\cos^2 a x} {\sin a x}$

$14.410$: Primitive of $\dfrac 1 {\cos a x \left({1 \pm \sin a x}\right)}$

$14.410.1$: Primitive of $\dfrac 1 {\cos a x \left({1 + \sin a x}\right)}$

$14.410.2$: Primitive of $\dfrac 1 {\cos a x \left({1 - \sin a x}\right)}$

$14.411$: Primitive of $\dfrac 1 {\sin a x \left({1 \pm \cos a x}\right)}$

$14.411.1$: Primitive of $\dfrac 1 {\sin a x \left({1 + \cos a x}\right)}$

$14.411.2$: Primitive of $\dfrac 1 {\sin a x \left({1 - \cos a x}\right)}$

$14.412$: Primitive of $\dfrac 1 {\sin a x \pm \cos a x}$

$14.412.1$: Primitive of $\dfrac 1 {\sin a x + \cos a x}$

$14.412.2$: Primitive of $\dfrac 1 {\sin a x \left({1 - \cos a x}\right)}$

$14.413$: Primitive of $\dfrac {\sin a x} {\sin a x \pm \cos a x}$

$14.413.1$: Primitive of $\dfrac {\sin a x} {\sin a x + \cos a x}$

$14.413.2$: Primitive of $\dfrac {\sin a x} {\sin a x \left({1 - \cos a x}\right)}$

$14.414$: Primitive of $\dfrac {\cos a x} {\sin a x \pm \cos a x}$

$14.414.1$: Primitive of $\dfrac {\cos a x} {\sin a x + \cos a x}$

$14.414.2$: Primitive of $\dfrac {\cos a x} {\sin a x \left({1 - \cos a x}\right)}$

$14.415$: Primitive of $\dfrac {\sin a x} {p + q \cos a x}$

$14.416$: Primitive of $\dfrac {\cos a x} {p + q \sin a x}$

$14.417$: Primitive of $\dfrac {\sin a x} {\left({p + q \cos a x}\right)^n}$

$14.418$: Primitive of $\dfrac {\cos a x} {\left({p + q \cos a x}\right)^n}$

$14.419$: Primitive of $\dfrac 1 {p \sin a x + q \cos a x}$

$14.420$: Primitive of $\dfrac 1 {p \sin a x + q \cos a x + r}$

[If $r = q$, see $14.421$: Primitive of $\dfrac 1 {p \sin a x + q \left({1 + \cos a x}\right)}$.

If $r^2 = p^2 + q^2$, see $14.422$: Primitive of $\dfrac 1 {p \sin a x + q \cos a x \pm \sqrt{p^2 + q^2}}$.]

$14.421$: Primitive of $\dfrac 1 {p \sin a x + q \left({1 + \cos a x}\right)}$

$14.422$: Primitive of $\dfrac 1 {p \sin a x + q \cos a x \pm \sqrt{p^2 + q^2}}$

$14.422.1$: Primitive of $\dfrac 1 {p \sin a x + q \cos a x + \sqrt{p^2 + q^2}}$

$14.422.2$: Primitive of $\dfrac 1 {p \sin a x + q \cos a x - \sqrt{p^2 + q^2}}$

$14.423$: Primitive of $\dfrac 1 {p^2 \sin^2 a x + q^2 \cos^2 a x}$

$14.424$: Primitive of $\dfrac 1 {p^2 \sin^2 a x - q^2 \cos^2 a x}$

$14.425$: Primitive of $\sin^m a x \cos^n a x$

$14.425.1$: Reduction of Power of Sine

$14.425.2$: Reduction of Power of Cosine

$14.426$: Primitive of $\dfrac {\sin^m a x} {\cos^n a x}$

$14.426.1$: Reduction of Both Powers

$14.426.2$: Reduction of Power of Sine

$14.426.3$: Reduction of Power of Cosine

$14.427$: Primitive of $\dfrac {\cos^m a x} {\sin^n a x}$

$14.427.1$: Reduction of Both Powers

$14.427.2$: Reduction of Power of Sine

$14.427.3$: Reduction of Power of Cosine

$14.428$: Primitive of $\dfrac 1 {\sin^m a x \cos^n a x}$

$14.428.1$: Reduction of Power of Cosine

$14.428.2$: Reduction of Power of Sine