 Matematica
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Integrali con $\small \tan(ax) $
- 1.
- $\displaystyle\int\tan ax dx=-\displaystyle \frac{1}{a}\ln\cos ax=\displaystyle \frac{1}{a}\ln\sec ax$
- 2.
- $\displaystyle\int\tan^2 ax dx=\displaystyle \frac{\tan ax}{a}-x$
- 3.
- $\displaystyle\int\tan^3 ax dx=\displaystyle \frac{\tan^2 ax}{2a}+\displaystyle \frac{1}{a}\ln\cos ax$
- 4.
- $\displaystyle\int\tan^n ax \sec^2 ax dx=\displaystyle \frac{\tan^{n+1}ax}{(n+1)a}$
- 5.
- $\displaystyle\int\displaystyle \frac{\sec^2 ax}{\tan ax}dx=\displaystyle \frac{1}{a}\ln\tan ax$
- 6.
- $\displaystyle\int\displaystyle \frac{dx}{\tan ax}=\displaystyle \frac{1}{a}\ln\sin ax$
- 7.
- $\displaystyle\int x\tan^2 ax dx=\displaystyle \frac{x\tan ax}{a}+\displaystyle \frac{1}{a^2}\ln\cos ax-\displaystyle \frac{x^2}{2}$
- 8.
- $\displaystyle\int\displaystyle \frac{dx}{p+q\tan ax}=\displaystyle \frac{px}{p^2+q^2}+\displaystyle \frac{q}{a(p^2+q^2)}\ln(q\sin ax+p\cos ax)$
- 9.
- $\displaystyle\int\tan^n ax dx=\displaystyle \frac{\tan^{n-1}ax}{(n-1)a}-\int\tan^{n-2}ax dx$
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