integral from pi to 2pi of (1+cos(x))/x

Lösung

\int_{π}^{2 π} \frac{1 + cos ( x )}{x} d x

ln (2) + Ci (2 π) - Ci (π)

Schritte zur Lösung

\int_{π}^{2 π} \frac{1 + cos ( x )}{x} d x

Multipliziere aus

\frac{1 + cos ( x )}{x} : \frac{1}{x} + \frac{cos ( x )}{x}

= \int_{π}^{2 π} \frac{1}{x} + \frac{cos ( x )}{x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{π}^{2 π} \frac{1}{x} d x + \int_{π}^{2 π} \frac{cos ( x )}{x} d x

\int_{π}^{2 π} \frac{1}{x} d x = ln (2)

\int_{π}^{2 π} \frac{cos ( x )}{x} d x = Ci (2 π) - Ci (π)

= ln (2) + Ci (2 π) - Ci (π)

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