INTEGRALS CONTAINING ax²+bx+c

1.

$$\int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}=\left\{\beg... ...{2ax+b+\displaystyle \sqrt{b^{\displaystyle2}-4ac}}\right) \end{array} \right.$$

2.

$$\int\displaystyle \frac{x\,dx}{ax^{\displaystyle2}+bx+c}=\display... ...\frac{b}{2a}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$$

3.

$$\int\displaystyle \frac{x^{\displaystyle2}\,dx}{ax^{\displaystyle... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$$

4.

$$\int\displaystyle \frac{x^{\displaystyle m}}{ax^{\displaystyle2}+... ...le \int\displaystyle \frac{x^{\displaystyle m-1}\,dx}{ax^{\displaystyle2}+bx+c}$$

5.

$$\int\displaystyle \frac{dx}{x(ax^{\displaystyle2}+bx+c)}=\display... ...\frac{b}{2c}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$$

6.

$$\int\displaystyle \frac{dx}{x^{\displaystyle2}(ax^{\displaystyle2... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$$

7.

$\begin{array}{ll} \displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle n}... ...laystyle \frac{dx}{x^{\displaystyle n-2}(ax^{\displaystyle2}+bx+c)} \end{array}$

8.

$$\int\displaystyle \frac{dx}{(ax^{\displaystyle2}+bx+c)^{\displays... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$$

9.

$$\int\displaystyle \frac{x\,dx}{(ax^{\displaystyle2}+bx+c)^{\displ... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$$

10.

$$\int\displaystyle \frac{x^{\displaystyle2}\,dx}{(ax^{\displaystyl... ...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$$

11.

$\begin{array}{ll} \displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx... ...isplaystyle m-2}\,dx}{(ax^{\displaystyle2}+bx+c)^{\displaystyle n}} \end{array}$

12.

$\begin{array}{ll} \displaystyle \int\displaystyle \frac{x^{\displaystyle2n-1}\,... ...isplaystyle2n-2}\,dx}{(ax^{\displaystyle2}+bx+c)^{\displaystyle n}} \end{array}$

13.

$\begin{array}{ll} \displaystyle \int\displaystyle \frac{dx}{x(ax^{\displaystyle... ...splaystyle \int\displaystyle \frac{dx}{x(ax^{\displaystyle2}+bx+c)} \end{array}$

14.

$\begin{array}{ll} \displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(... ...isplaystyle \frac{dx}{x(ax^{\displaystyle2}+bx+c)^{\displaystyle2}} \end{array}$

15.

$\begin{array}{lcl} \displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m... ...{x^{\displaystyle m-1}(ax^{\displaystyle2}+bx+c)^{\displaystyle n}} \end{array}$

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