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Beliebt Rechnen >

integral of (7sin(x)+2sec(x))/(tan(x))

Lösung

\int \frac{7 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

Lösung

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

Schritte zur Lösung

\int \frac{7 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

Multipliziere aus

\frac{7 sin ( x ) + 2 sec ( x )}{tan ( x )} : \frac{7 sin ( x )}{tan ( x )} + \frac{2 sec ( x )}{tan ( x )}

= \int \frac{7 sin ( x )}{tan ( x )} + \frac{2 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{7 sin ( x )}{tan ( x )} d x + \int \frac{2 sec ( x )}{tan ( x )} d x

\int \frac{7 sin ( x )}{tan ( x )} d x = 7 sin (x)

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

= 7 sin (x) + 2 ln tan (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= 7 sin (x) + 2 ln tan (\frac{x}{2}) + C

Graph

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\frac{\partial}{\partial x} (\frac{5}{x y} + \frac{x}{y} + \frac{y}{x})

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\int x \cdot e^{5 x} d x

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