INTEGRALS CONTAINING ax2+bx+c

1.
$\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}=\left\{\beg...
...{2ax+b+\displaystyle \sqrt{b^{\displaystyle2}-4ac}}\right)
\end{array} \right.$

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

3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{ax^{\displaystyle...
...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$

4.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}}{ax^{\displaystyle2}+...
...le \int\displaystyle \frac{x^{\displaystyle m-1}\,dx}{ax^{\displaystyle2}+bx+c}$

5.
$\displaystyle \int\displaystyle \frac{dx}{x(ax^{\displaystyle2}+bx+c)}=\display...
...\frac{b}{2c}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$

6.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle2}(ax^{\displaystyle2...
...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$

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

9.
$\displaystyle \int\displaystyle \frac{x\,dx}{(ax^{\displaystyle2}+bx+c)^{\displ...
...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$

10.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle2}\,dx}{(ax^{\displaystyl...
...playstyle2}}\displaystyle \int\displaystyle \frac{dx}{ax^{\displaystyle2}+bx+c}$

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

[Tables]

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