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

1.

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

2.

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

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.

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

5.

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

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