de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

Beliebte Beispiele

derivative x^{0.5}

d er i v a t i v e x^{0.5}

derivative of xsin(pix)

\frac{d}{d x} (x sin (π x))

derivative of 9e^x(cos(x-sin(x)))

\frac{d}{d x} (9 e^{x} (cos (x) - sin (x)))

integral of (cos(x)+5^x)

\int (cos (x) + 5^{x}) d x

integral of (x^2+6x)cos(x)

\int (x^{2} + 6 x) cos (x) d x