INTEGRALS CONTAINING THE SQUARE ROOT OF ax+b AND px+q

1.

$\displaystyle \int\displaystyle \frac{px+q}{\displaystyle \sqrt{ax+b}}\,dx=\displaystyle \frac{2(apx+3aq-2bp)}{3a^{\displaystyle2 }}\displaystyle \sqrt{ax+b}$

2.

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

3.

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

4.

$\displaystyle \int(px+q)^{\displaystyle n}\displaystyle \sqrt{ax+b}\,dx=\displa... ...int\displaystyle \frac{(px+q)^{\displaystyle n}}{\displaystyle \sqrt{ax+b}}\,dx$

5.

$\displaystyle \int\displaystyle \frac{(px+q)^{\displaystyle n}}{\displaystyle \... ...t\displaystyle \frac{(px+q)^{\displaystyle n-1}\,dx}{\displaystyle \sqrt{ax+b}}$

6.

$\displaystyle \int\displaystyle \frac{\displaystyle \sqrt{ax+b}}{(px+q)^{\displ... ...int\displaystyle \frac{dx}{(px+q)^{\displaystyle n-1}\displaystyle \sqrt{ax+b}}$

7.

$\displaystyle \begin{array}{l} \displaystyle \int\displaystyle \frac{dx}{(px+q... ...frac{dx}{(px+q)^{\displaystyle n-1}\displaystyle \sqrt{ax+b}}\right.\end{array}$