Table of Integrals, Series, and Products, 8th Edition

$\left[\begin{array}{lll}0\le b<n,\hfill & n\ge 1,\hfill & r=\left(n-b\right)/2\hfill \end{array}\right]$

6.¹¹ 

$\begin{array}{ll}{\displaystyle {\int }_0^{\infty }{\left(\frac{sinx}{x}\right)}^{n}cosanx\text{d}x=0}\hfill & \left[\begin{array}{llll}a\le -1\text{or}a\ge \text{1,}\hfill & n\ge 2;\hfill & \text{for}\hfill & n=1\text{see}3.741\text{2}\hfill \end{array}\right]\hfill \end{array}$

3.837

1. 

${\displaystyle {\int }_0^{\pi /2}\frac{x^2\text{d}x}{{sin}^{2}x}}=\pi \ln 2$

  BI (206)(9)

2. 

${\displaystyle {\int }_0^{\pi /4}\frac{x^2\text{d}x}{{sin}^{2}x}}=-\frac{{\pi }^2}{16}+\frac{\pi }{4}\ln 2+G$

  BI (204)(10)

3. 

${\displaystyle {\int }_0^{\pi /4}\frac{x^2\text{d}x}{{cos}^{2}x}}=\frac{{\pi }^2}{16}+\frac{\pi }{4}\ln 2-G$

  GW (333)(35a)

4. 

${\displaystyle {\int }_0^{\pi /4}\frac{x^{p+1}}{{sin}^{2}x}\text{d}x}=$