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

1.

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

2.

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

3.

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

4.

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

5.

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

6.

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

7.

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

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