Übung
$\int\frac{9x-8}{\left(x-3\right)\left(2x+5\right)}dx$
Schritt-für-Schritt-Lösung
Learn how to solve problems step by step online. int((9x-8)/((x-3)(2x+5)))dx. Rewrite the fraction \frac{9x-8}{\left(x-3\right)\left(2x+5\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{19}{11\left(x-3\right)}+\frac{61}{11\left(2x+5\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{19}{11\left(x-3\right)}dx results in: \frac{19}{11}\ln\left(x-3\right). The integral \int\frac{61}{11\left(2x+5\right)}dx results in: \frac{61}{22}\ln\left(2x+5\right).
int((9x-8)/((x-3)(2x+5)))dx
Endgültige Antwort auf das Problem
$\frac{19}{11}\ln\left|x-3\right|+\frac{61}{22}\ln\left|2x+5\right|+C_0$