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3.6: Додаткові методи інтеграції
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\[ \begin{align*} \int \frac{1}{x^2-a^2}\, dx & = \frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right|+C \\ \int \frac{1}{\sqrt{x^2+a^2}}\, dx & = \ln\left|x+\sqrt{x^2+a^2}\right|+C \end{align*} \nonumber \] Т...\[ \begin{align*} \int \frac{1}{x^2-a^2}\, dx & = \frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right|+C \\ \int \frac{1}{\sqrt{x^2+a^2}}\, dx & = \ln\left|x+\sqrt{x^2+a^2}\right|+C \end{align*} \nonumber \] Тепер просто використовуємо формулу з таблиці, з\(a = 3\). \[ \begin{align*} \int\frac{5}{x^2-9}\, dx = & 5\int\frac{1}{x^2-3^2}\, dx \\ & = 5\left(\frac{1}{2\cdot 3}\ln\left|\frac{x-3}{x+3}\right|\right)+C \\ & = \frac{5}{6}\ln\left|\frac{x-3}{x+3}\right|+C \end{align*} \nonumber \]