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Beliebt Rechnen >

integral (1+x)cos(1+x)

Lösung

integral

(1 + x) cos (1 + x)

Lösung

sin (1 + x) + x sin (1 + x) + cos (1 + x) + C

Schritte zur Lösung

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

Multipliziere aus

(1 + x) cos (1 + x) : cos (1 + x) + x cos (1 + x)

= \int cos (1 + x) + x cos (1 + x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (1 + x) d x + \int x cos (1 + x) d x

\int cos (1 + x) d x = sin (1 + x)

\int x cos (1 + x) d x = x sin (1 + x) + cos (1 + x)

= sin (1 + x) + x sin (1 + x) + cos (1 + x)

Füge eine Konstante zur Lösung hinzu

= sin (1 + x) + x sin (1 + x) + cos (1 + x) + C

Graph

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