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Beliebt Rechnen >

integral of cos(ln(x))ln(x)

Lösung

\int cos (ln (x)) ln (x) d x

Lösung

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

Schritte zur Lösung

\int cos (ln (x)) ln (x) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral from 0 to 3 of (x^2-5)/(x+2)

\int_{0}^{3} \frac{x ^{2} - 5}{x + 2} d x

integral of (x/(sqrt(1-x^2)))

\int (\frac{x}{1 - x ^{2}}) d x

integral from-4 to 0 of |x+2|

\int_{- 4}^{0} ∣ x + 2 ∣ d x

(\partial)/(\partial x)(4-x^2-2y^2)

\frac{\partial}{\partial x} (4 - x^{2} - 2 y^{2})

derivative of Ax^2e^{3x}

\frac{d}{d x} (A x^{2} e^{3 x})