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Beliebt Rechnen >

integral of ((9sin(x)+4sec(x)))/(tan(x))

Lösung

\int \frac{( 9 sin ( x ) + 4 sec ( x ) )}{tan ( x )} d x

Lösung

9 sin (x) + 4 ln tan (\frac{x}{2}) + C

Schritte zur Lösung

\int \frac{9 sin ( x ) + 4 sec ( x )}{tan ( x )} d x

Multipliziere aus

\frac{9 sin ( x ) + 4 sec ( x )}{tan ( x )} : \frac{9 sin ( x )}{tan ( x )} + \frac{4 sec ( x )}{tan ( x )}

= \int \frac{9 sin ( x )}{tan ( x )} + \frac{4 sec ( x )}{tan ( 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 \frac{9 sin ( x )}{tan ( x )} d x + \int \frac{4 sec ( x )}{tan ( x )} d x

\int \frac{9 sin ( x )}{tan ( x )} d x = 9 sin (x)

\int \frac{4 sec ( x )}{tan ( x )} d x = 4 ln tan (\frac{x}{2})

= 9 sin (x) + 4 ln tan (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= 9 sin (x) + 4 ln tan (\frac{x}{2}) + C

Graph

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