integral (1/x)(cos(x)-sin(x))

Lösung

integral

(\frac{1}{x}) (cos (x) - sin (x))

Ci (x) - Si (x) + C

Schritte zur Lösung

\int \frac{1}{x} (cos (x) - sin (x)) d x

Vereinfache

\frac{1}{x} (cos (x) - sin (x)) : \frac{cos ( x ) - sin ( x )}{x}

= \int \frac{cos ( x ) - sin ( x )}{x} d x

Multipliziere aus

\frac{cos ( x ) - sin ( x )}{x} : \frac{cos ( x )}{x} - \frac{sin ( x )}{x}

= \int \frac{cos ( x )}{x} - \frac{sin ( x )}{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{cos ( x )}{x} d x - \int \frac{sin ( x )}{x} d x

\int \frac{cos ( x )}{x} d x = Ci (x)

\int \frac{sin ( x )}{x} d x = Si (x)

= Ci (x) - Si (x)

Füge eine Konstante zur Lösung hinzu

= Ci (x) - Si (x) + C

in t e g r a l \frac{( x + 7 )}{( x + 9 )}

in t e g r a l sin (1 - x)

in t e g r a l cos (y^{2})

in t e g r a l sin (2 x + y)

in t e g r a l f (x) = 55 - 4 x