integral of sin(x)ln(c)osx

Lösung

\int sin (x) ln (c) os x d x

os ln (c) (- x cos (x) + sin (x)) + C

Schritte zur Lösung

\int sin (x) ln (c) os x d x

Entferne die Konstante:

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

= ln (c) os \cdot \int sin (x) x d x

Wende die partielle Integration an

= ln (c) os (- x cos (x) - \int - cos (x) d x)

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

= ln (c) os (- x cos (x) - (- sin (x)))

Vereinfache

= os ln (c) (- x cos (x) + sin (x))

Füge eine Konstante zur Lösung hinzu

= os ln (c) (- x cos (x) + sin (x)) + C

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