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Beliebt Rechnen >

integral of (tan(x)+sec(x))/(sec^2(x))

Lösung

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

Lösung

\frac{sin ^{2} ( x )}{2} + sin (x) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{tan ( x ) + sec ( x )}{sec ^{2} ( x )} : \frac{tan ( x )}{sec ^{2} ( x )} + \frac{1}{sec ( x )}

= \int \frac{tan ( x )}{sec ^{2} ( x )} + \frac{1}{sec ( 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{tan ( x )}{sec ^{2} ( x )} d x + \int \frac{1}{sec ( x )} d x

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

\int \frac{1}{sec ( x )} d x = sin (x)

= \frac{sin ^{2} ( x )}{2} + sin (x)

Füge eine Konstante zur Lösung hinzu

= \frac{sin ^{2} ( x )}{2} + sin (x) + C

Graph

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