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

Lösung

\int + \frac{2 cot ( x ) - 3 sin ^{2} ( x )}{sin ( x )} d x

- 2 csc (x) + 3 cos (x) + C

Schritte zur Lösung

\int \frac{2 cot ( x ) - 3 sin ^{2} ( x )}{sin ( x )} d x

Multipliziere aus

\frac{2 cot ( x ) - 3 sin ^{2} ( x )}{sin ( x )} : \frac{2 cot ( x )}{sin ( x )} - 3 sin (x)

= \int \frac{2 cot ( x )}{sin ( x )} - 3 sin (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{2 cot ( x )}{sin ( x )} d x - \int 3 sin (x) d x

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

\int 3 sin (x) d x = - 3 cos (x)

= - 2 csc (x) - (- 3 cos (x))

Vereinfache

= - 2 csc (x) + 3 cos (x)

Füge eine Konstante zur Lösung hinzu

= - 2 csc (x) + 3 cos (x) + C

\int 1 - \frac{1}{cos ^{2} ( 2 x )} d x

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\int \frac{2 x + 1}{( x + 2 ) ^{4} ( x - 1 ) ^{4}} d x

\int \frac{1}{1 - e ^{2 y}} d y