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Beliebt Rechnen >

integral of (sin(x)+cos(x))/(sin(2x))

Lösung

\int \frac{sin ( x ) + cos ( x )}{sin ( 2 x )} d x

Lösung

\frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + \frac{1}{2} ln tan (\frac{x}{2}) + C

Schritte zur Lösung

\int \frac{sin ( x ) + cos ( x )}{sin ( 2 x )} d x

Multipliziere aus

\frac{sin ( x ) + cos ( x )}{sin ( 2 x )} : \frac{sin ( x )}{sin ( 2 x )} + \frac{cos ( x )}{sin ( 2 x )}

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

\int \frac{sin ( x )}{sin ( 2 x )} d x = \frac{1}{2} ln ∣ tan (x) + sec (x) ∣

\int \frac{cos ( x )}{sin ( 2 x )} d x = \frac{1}{2} ln tan (\frac{x}{2})

= \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + \frac{1}{2} ln tan (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln ∣ tan (x) + sec (x) ∣ + \frac{1}{2} ln tan (\frac{x}{2}) + C

Graph

Beliebte Beispiele

integral of (x+2)/(x^3-2x^2)

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

integral of x^7sqrt(x^4+1)

\int x^{7} x^{4} + 1 d x

integral of (12x^2-4x+7)/(3x+1)

\int \frac{12 x ^{2} - 4 x + 7}{3 x + 1} d x

integral of ((1+x^{1/3})^3)/(sqrt(x))

\int \frac{( 1 + x ^{\frac{1}{3}} ) ^{3}}{x} d x

integral of 1/(x+2sqrt(x)+3)

\int \frac{1}{x + 2 x + 3} d x