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

Lösung

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

ln tan (\frac{x}{2}) - csc (x) + 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{1}{sin ( x )} + \frac{cos ( x )}{sin ^{2} ( x )}

= \int \frac{1}{sin ( 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{1}{sin ( x )} d x + \int \frac{cos ( x )}{sin ^{2} ( x )} d x

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

\int \frac{cos ( x )}{sin ^{2} ( x )} d x = - csc (x)

= ln tan (\frac{x}{2}) - csc (x)

Füge eine Konstante zur Lösung hinzu

= ln tan (\frac{x}{2}) - csc (x) + C

\int a rco sin (x) d x

t an g e n t x^{2} - 3

f (x) = x^{2} - cos (2 x)

\frac{d}{d x} (ln ((x^{2} + 1)^{2}))

t an g e n t y = x^{2} - 5, (2, - 1)