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Beliebt Rechnen >

integral of 3sin(ln(x))

Lösung

\int 3 sin (ln (x)) d x

Lösung

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

Schritte zur Lösung

\int 3 sin (ln (x)) d x

Entferne die Konstante:

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

= 3 \cdot \int sin (ln (x)) d x

Wende die partielle Integration an

= 3 (x sin (ln (x)) - \int cos (ln (x)) d x)

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

= 3 (x sin (ln (x)) - (\frac{1}{2} x sin (ln (x)) + \frac{1}{2} x cos (ln (x))))

Multipliziere aus

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

= 3 (\frac{1}{2} x sin (ln (x)) - \frac{1}{2} x cos (ln (x)))

Füge eine Konstante zur Lösung hinzu

= 3 (\frac{1}{2} x sin (ln (x)) - \frac{1}{2} x cos (ln (x))) + C

Graph

Beliebte Beispiele

integral from 0 to x of e^t

\int_{0}^{x} e^{t} d t

derivative y^{-1}+y^{-2}

d er i v a t i v e y^{- 1} + y^{- 2}

integral from-1 to 0 of |x^2-1|

\int_{- 1}^{0} x^{2} - 1 d x

limit as x approaches-9+of 1/(x+9)

x \to - 9 + lim (\frac{1}{x + 9})

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t an g e n t y = 6 x^{2} - x^{3} (1.5)