Kenan Kılıçaslan

\(\tan(a x)\) içeren integraller

Bu sayfa, \(\tan(a x)\) biçimindeki trigonometrik fonksiyonları içeren belirsiz integral formüllerini sunar. Bu integraller genellikle trigonometrik dönüşümler ve logaritmik ifadeler kullanılarak çözülür.

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