Logarithmische Integration
Beispiele
\(\int \frac{1}{x}\, \mathrm dx = \int \frac{x'}{x} \mathrm\, dx = \ln(|x|) +c,\,c\in\mathbb{R} \).
\(\int \frac{3x^2 + 17}{x^3 +17x - 15}\, \mathrm dx = \ln(|x^3 + 17x - 15|)+c,\,c\in\mathbb{R}\). \(\int \frac{\cos(x)}{\sin(x)}\,\mathrm dx = \ln(|\sin(x)|)+c,\,c\in\mathbb{R}\).
\(\int \frac{1}{x}\, \mathrm dx = \int \frac{x'}{x} \mathrm\, dx = \ln(|x|) +c,\,c\in\mathbb{R} \).
\(\int \frac{3x^2 + 17}{x^3 +17x - 15}\, \mathrm dx = \ln(|x^3 + 17x - 15|)+c,\,c\in\mathbb{R}\). \(\int \frac{\cos(x)}{\sin(x)}\,\mathrm dx = \ln(|\sin(x)|)+c,\,c\in\mathbb{R}\).
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