INTEGRALS CONTAINING THE SQUARE ROOTS OF BOTH ax+b AND px+q

1.
$\displaystyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{(ax+b)(px+q)}}=\l...
...displaystyle \sqrt{\displaystyle \frac{-p(ax+b)}{a(px+q)}}
\end{array} \right.$

2.
$\displaystyle \int\displaystyle \frac{x\,dx}{\displaystyle \sqrt{(ax+b)(px+q)}}...
...ap}\displaystyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{(ax+b)(px+q)}}$

3.
$\begin{array}{lcl}
\displaystyle \int\displaystyle \sqrt{(ax+b)(px+q)}\,dx&=&\d...
...style \int\displaystyle \frac{dx}{\displaystyle \sqrt{(ax+b)(px+q)}}\end{array}$

4.
$\displaystyle \int\displaystyle \sqrt{\displaystyle \frac{px+q}{ax+b}}\,dx=\dis...
...2a}\displaystyle \int\displaystyle \frac{dx}{\displaystyle \sqrt{(ax+b)(px+q)}}$

5.
$\displaystyle \int\displaystyle \frac{dx}{(px+q)\displaystyle \sqrt{(ax+b)(px+q...
...isplaystyle \frac{2\displaystyle \sqrt{ax+b}}{(aq-bp)\displaystyle \sqrt{px+q}}$

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