integral of (cos(x))/(x^3)

Lösung

\int \frac{cos ( x )}{x ^{3}} d x

- \frac{cos ( x )}{2 x ^{2}} - \frac{1}{2} (- \frac{sin ( x )}{x} + Ci (x)) + C

Schritte zur Lösung

\int \frac{cos ( x )}{x ^{3}} d x

Wende die partielle Integration an

= - \frac{cos ( x )}{2 x ^{2}} - \int \frac{sin ( x )}{2 x ^{2}} d x

\int \frac{sin ( x )}{2 x ^{2}} d x = \frac{1}{2} (- \frac{sin ( x )}{x} + Ci (x))

= - \frac{cos ( x )}{2 x ^{2}} - \frac{1}{2} (- \frac{sin ( x )}{x} + Ci (x))

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ( x )}{2 x ^{2}} - \frac{1}{2} (- \frac{sin ( x )}{x} + Ci (x)) + C

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