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Beliebt Rechnen >

integral of (1+1/(sin^2(x)))cos(x)

Lösung

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

Lösung

sin (x) - csc (x) + C

Schritte zur Lösung

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

Multipliziere aus

(1 + \frac{1}{sin ^{2} ( x )}) cos (x) : cos (x) + \frac{cos ( x )}{sin ^{2} ( x )}

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

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

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

= sin (x) - csc (x)

Füge eine Konstante zur Lösung hinzu

= sin (x) - csc (x) + C

Graph

Beliebte Beispiele

integral of (cot(x))/(cos^2(x))

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

integral of (3x^2+9x+1)/x

\int \frac{3 x ^{2} + 9 x + 1}{x} d x

integral of 1/(sin(ax)cos(ax))

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

integral of sin(hx)

\int sin (h x) d x

integral of (24)/(1+9x^2)

\int \frac{24}{1 + 9 x ^{2}} d x