integral of 5arctan(4x)

Lösung

\int 5 arctan (4 x) d x

5 (x arctan (4 x) - \frac{1}{8} ln 16 x^{2} + 1) + C

Schritte zur Lösung

\int 5 arctan (4 x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int arctan (4 x) d x

Wende die partielle Integration an

= 5 (x arctan (4 x) - \int \frac{4 x}{16 x ^{2} + 1} d x)

\int \frac{4 x}{16 x ^{2} + 1} d x = \frac{1}{8} ln 16 x^{2} + 1

= 5 (x arctan (4 x) - \frac{1}{8} ln 16 x^{2} + 1)

Füge eine Konstante zur Lösung hinzu

= 5 (x arctan (4 x) - \frac{1}{8} ln 16 x^{2} + 1) + C

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