integral of 4xsinh(2x)

Lösung

\int 4 x sinh (2 x) d x

2 x cosh (2 x) - sinh (2 x) + C

Schritte zur Lösung

\int 4 x sinh (2 x) d x

Entferne die Konstante:

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

= 4 \cdot \int x sinh (2 x) d x

Wende die partielle Integration an

= 4 (\frac{1}{2} x cosh (2 x) - \int \frac{1}{2} cosh (2 x) d x)

\int \frac{1}{2} cosh (2 x) d x = \frac{1}{4} sinh (2 x)

= 4 (\frac{1}{2} x cosh (2 x) - \frac{1}{4} sinh (2 x))

Vereinfache

4 (\frac{1}{2} x cosh (2 x) - \frac{1}{4} sinh (2 x)) : 2 x cosh (2 x) - sinh (2 x)

= 2 x cosh (2 x) - sinh (2 x)

Füge eine Konstante zur Lösung hinzu

= 2 x cosh (2 x) - sinh (2 x) + C

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