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Beliebt Rechnen >

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

Lösung

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

Lösung

- cot (x) - \frac{1}{x} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

= - cot (x) - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= - cot (x) - \frac{1}{x} + C

Graph

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