integral of sin(2ln(x))

Lösung

\int sin (2 ln (x)) d x

\frac{1}{5} x sin (2 ln (x)) - \frac{2}{5} x cos (2 ln (x)) + C

Schritte zur Lösung

\int sin (2 ln (x)) d x

Wende die partielle Integration an

= x sin (2 ln (x)) - \int 2 cos (2 ln (x)) d x

\int 2 cos (2 ln (x)) d x = 2 (\frac{2}{5} x sin (2 ln (x)) + \frac{1}{5} x cos (2 ln (x)))

= x sin (2 ln (x)) - 2 (\frac{2}{5} x sin (2 ln (x)) + \frac{1}{5} x cos (2 ln (x)))

Vereinfache

x sin (2 ln (x)) - 2 (\frac{2}{5} x sin (2 ln (x)) + \frac{1}{5} x cos (2 ln (x))) : \frac{1}{5} x sin (2 ln (x)) - \frac{2}{5} x cos (2 ln (x))

= \frac{1}{5} x sin (2 ln (x)) - \frac{2}{5} x cos (2 ln (x))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} x sin (2 ln (x)) - \frac{2}{5} x cos (2 ln (x)) + C

\int (2 x + 1) cos (4 x) d x

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in t e g r a l 3 x

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