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Beliebt Rechnen >

integral of (sec(x)+cos(x))/(3cos(x))

Lösung

\int \frac{sec ( x ) + cos ( x )}{3 cos ( x )} d x

Lösung

\frac{1}{3} (tan (x) + x) + C

Schritte zur Lösung

\int \frac{sec ( x ) + cos ( x )}{3 cos ( x )} d x

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int \frac{sec ( x ) + cos ( x )}{cos ( x )} d x

Multipliziere aus

\frac{sec ( x ) + cos ( x )}{cos ( x )} : \frac{sec ( x )}{cos ( x )} + 1

= \frac{1}{3} \cdot \int \frac{sec ( x )}{cos ( x )} + 1 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

= \frac{1}{3} (\int \frac{sec ( x )}{cos ( x )} d x + \int 1 d x)

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

\int 1 d x = x

= \frac{1}{3} (tan (x) + x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} (tan (x) + x) + C

Graph

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