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Beliebt Rechnen >

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

Lösung

integral

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

Lösung

- \frac{1}{2} arctan (2 tan (x)) + x + C

Schritte zur Lösung

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

\frac{sin ^{2} ( x )}{1 + sin ^{2} ( x )} = - \frac{1}{1 + sin ^{2} ( x )} + 1

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

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

\int 1 d x = x

= - \frac{1}{2} arctan (2 tan (x)) + x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} arctan (2 tan (x)) + x + C

Graph

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