Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 15/Definite Integrals involving Trigonometric Functions

Definite Integrals involving Trigonometric Functions

 * $15.26$: Definite Integral from $0$ to $\pi$ of $\sin m x \sin n x$


 * $15.27$: Definite Integral from $0$ to $\pi$ of $\cos m x \cos n x$


 * $15.28$: Definite Integral from $0$ to $\pi$ of $\sin m x \cos n x$


 * $15.29$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^2 x$ and $\cos^2 x$
 * $15.29.1$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^2 x$
 * $15.29.2$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\cos^2 x$


 * $15.30$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^{2 n} x$ and $\cos^{2 n} x$
 * $15.30.1$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^{2 n} x$
 * $15.30.2$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\cos^{2 n} x$


 * $15.31$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^{2 n + 1} x$ and $\cos^{2 n + 1} x$
 * $15.31.1$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^{2 n + 1} x$
 * $15.31.2$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\cos^{2 n + 1} x$


 * $15.32$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\sin^{2 p - 1} x \cos^{2 p - 1} x$


 * $15.33$: Definite Integral to Infinity of $\dfrac {\sin p x} x$


 * $15.34$: Definite Integral to Infinity of $\dfrac {\sin p x \cos q x} x$


 * $15.35$: Definite Integral to Infinity of $\dfrac {\sin p x \sin q x} {x^2}$


 * $15.36$: Definite Integral to Infinity of $\paren {\dfrac {\sin p x} x}^2$


 * $15.37$: Definite Integral to Infinity of $\dfrac {1 - \cos p x} {x^2}$


 * $15.38$: Definite Integral to Infinity of $\dfrac {\cos p x - \cos q x} x$


 * $15.39$: Definite Integral to Infinity of $\dfrac {\cos p x - \cos q x} {x^2}$


 * $15.40$: Definite Integral to Infinity of $\dfrac {\cos m x} {x^2 + a^2}$


 * $15.41$: Definite Integral to Infinity of $\dfrac {x \sin m x} {x^2 + a^2}$


 * $15.42$: Definite Integral to Infinity of $\dfrac {\sin m x} {x \paren {x^2 + a^2} }$


 * $15.43$: Definite Integral from $0$ to $2 \pi$ of $\dfrac 1 {a + b \sin x}$


 * $15.44$: Definite Integral from $0$ to $2 \pi$ of $\dfrac 1 {a + b \cos x}$


 * $15.45$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\dfrac 1 {a + b \cos x}$


 * $15.46$: Definite Integral from 0 to $2 \pi$ of $\dfrac 1 {\paren {a + b \sin x}^2}$ and $\dfrac 1 {\paren {a + b \cos x}^2}$
 * $15.46.1$: Definite Integral from $0$ to $2 \pi$ of $\dfrac 1 {\paren {a + b \sin x}^2}$
 * $15.46.2$: Definite Integral from $0$ to $2 \pi$ of $\dfrac 1 {\paren {a + b \cos x}^2}$


 * $15.47$: Definite Integral from $0$ to $2 \pi$ of $\dfrac 1 {1 - 2 a \cos x + a^2}$


 * $15.48$: Definite Integral from $0$ to $2 \pi$ of $\dfrac {x \sin x} {1 - 2 a \cos x + a^2}$


 * $15.49$: Definite Integral from $0$ to $\pi$ of $\dfrac {\cos m x} {1 - 2 a \cos x + a^2}$


 * $15.50$: Definite Integral to Infinity of $\sin a x^2$ and $\cos a x^2$
 * $15.50.1$: Definite Integral to Infinity of $\sin a x^2$
 * $15.50.2$: Definite Integral to infinity of $\cos a x^2$


 * $15.51$: Definite Integral to Infinity of $\sin a x^n$


 * $15.52$: Definite Integral to Infinity of $\cos a x^n$


 * $15.53$: Definite Integral to Infinity of $\dfrac {\sin x} {\sqrt x}$ and $\dfrac {\cos x} {\sqrt x}$
 * $15.53.1$: Definite Integral to Infinity of $\dfrac {\sin x} {\sqrt x}$
 * $15.53.2$: Definite Integral to Infinity of $\dfrac {\cos x} {\sqrt x}$


 * $15.54$: Definite Integral to Infinity of $\dfrac {\sin x} {x^p}$


 * $15.55$: Definite Integral to Infinity of $\dfrac {\cos x} {x^p}$


 * $15.56$: Definite Integral to Infinity of $\sin a x^2 \cos 2 b x$


 * $15.57$: Definite Integral to Infinity of $\cos a x^2 \cos 2 b x$


 * $15.58$: Definite Integral to Infinity of $\dfrac {\sin^3 x} {x^3}$


 * $15.59$: Definite Integral to Infinity of $\dfrac {\sin^4 x} {x^4}$


 * $15.60$: Definite Integral to Infinity of $\dfrac {\tan x} x$


 * $15.61$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\dfrac 1 {1 + \tan^m x}$


 * $15.62$: Definite Integral from $0$ to $\dfrac \pi 2$ of $\dfrac x {\sin x}$


 * $15.63$: Definite Integral from $0$ to $1$ of $\dfrac {\arctan x} x$


 * $15.64$: Definite Integral from $0$ to $1$ of $\dfrac {\arcsin x} x$


 * $15.65$: Euler-Mascheroni Constant as Difference of Integrals involving Cosine


 * $15.66$: Definite Integral to Infinity of $\paren {\dfrac 1 {1 + x^2} - \cos x} \dfrac 1 x$


 * $15.67$: Definite Integral to Infinity of $\dfrac {\arctan p x - \arctan q x} x$