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

Lösung

\int \frac{1}{9} csc^{2} (x) + \frac{1}{x ^{2}} d x

- \frac{1}{9} cot (x) - \frac{1}{x} + C

Schritte zur Lösung

\int \frac{1}{9} csc^{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}{9} csc^{2} (x) d x + \int \frac{1}{x ^{2}} d x

\int \frac{1}{9} csc^{2} (x) d x = - \frac{1}{9} cot (x)

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

= - \frac{1}{9} cot (x) - \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{9} cot (x) - \frac{1}{x} + C

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

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