INTEGRALS CONTAINING "xn+an" or "xn-an"

1.
$\displaystyle \int\displaystyle \frac{dx}{x\left(x^{\displaystyle n}+a^{\displa...
...isplaystyle \frac{x^{\displaystyle n}}{x^{\displaystyle n}+a^{\displaystyle n}}$

2.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle n-1}\,dx}{x^{\displaysty...
...displaystyle \frac{1}{n}\ln\left(x^{\displaystyle n}+a^{\displaystyle n}\right)$

3.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx}{\left(x^{\displa...
...n}\,dx}{\left(x^{\displaystyle n}+a^{\displaystyle n}\right)^{\displaystyle r}}$

4.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m}\left(x^{\displays...
...yle m-n}\left(x^{\displaystyle n}+a^{\displaystyle n}\right)^{\displaystyle r}}$

5.
$\displaystyle \int\displaystyle \frac{dx}{x\displaystyle \sqrt{x^{\displaystyle...
...ystyle n}+a^{\displaystyle n}}+\displaystyle \sqrt{a^{\displaystyle n}}}\right)$

6.
$\displaystyle \int\displaystyle \frac{dx}{x\left(x^{\displaystyle n}-a^{\displa...
...tyle \frac{x^{\displaystyle n}-a^{\displaystyle n}}{x^{\displaystyle n}}\right)$

7.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle n-1}\,dx}{x^{\displaysty...
...displaystyle \frac{1}{n}\ln\left(x^{\displaystyle n}-a^{\displaystyle n}\right)$

8.
$\displaystyle \int\displaystyle \frac{x^{\displaystyle m}\,dx}{\left(x^{\displa...
...\,dx}{\left(x^{\displaystyle n}-a^{\displaystyle n}\right)^{\displaystyle r-1}}$

9.
$\displaystyle \int\displaystyle \frac{dx}{x^{\displaystyle m}\left(x^{\displays...
...yle m}\left(x^{\displaystyle n}-a^{\displaystyle n}\right)^{\displaystyle r-1}}$

10.
$\displaystyle \int\displaystyle \frac{dx}{x\displaystyle \sqrt{x^{\displaystyle...
...splaystyle \sqrt{\displaystyle \frac{a^{\displaystyle n}}{x^{\displaystyle n}}}$

11.
$\displaystyle
\begin{array}{lcl}
\displaystyle \int\displaystyle \frac{x^{\disp...
...\cos\displaystyle \frac{(2k-1)\pi}{2m}+a^{\displaystyle2}\right)\\
\end{array}$

where $0<p\leq 2m$.

12.
$\displaystyle
\begin{array}{lcl}
\displaystyle \int\displaystyle \frac{x^{\disp...
...^{\displaystyle2m-p}}\{\ln(x-a)+(-1)^{\displaystyle p}\ln(x+a)\}\\
\end{array}$

where $0<p\leq 2m$.

13.
$\displaystyle
\begin{array}{ll}
\displaystyle \int\displaystyle \frac{x^{\displ...
...(-1)^{\displaystyle p-1}\ln(x+a)}{(2m+1)a^{\displaystyle2m-p+1}}\\
\end{array}$

where $0<p\leq2m+1$.

14.
$\displaystyle\begin{array}{ll}
\displaystyle \int\displaystyle \frac{x^{\displa...
...} }+\displaystyle \frac{\ln(x-a)}{(2m+1)a^{\displaystyle2m-p+1}}\\
\end{array}$

where $0<p\leq2m+1$.

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