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Beliebt Rechnen >

integral of (sin(x)+cos(x))/(tan(x))

Lösung

\int \frac{sin ( x ) + cos ( x )}{tan ( x )} d x

Lösung

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

Schritte zur Lösung

\int \frac{sin ( x ) + cos ( x )}{tan ( x )} d x

Multipliziere aus

\frac{sin ( x ) + cos ( x )}{tan ( x )} : \frac{sin ( x )}{tan ( x )} + \frac{cos ( x )}{tan ( x )}

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 6x^5e^{8x^6}

\int 6 x^{5} e^{8 x^{6}} d x

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d er i v a t i v e \frac{3 x ^{2} - 9 x + 13}{3 x + 4}

integral of-x^2+4x-3

\int - x^{2} + 4 x - 3 d x

derivative of 9tan(x)

\frac{d}{d x} (9 tan (x))

(\partial)/(\partial x)((10x)/(1+x^2-y))

\frac{\partial}{\partial x} (\frac{10 x}{1 + x ^{2} - y})