integral of ((x+3))/(sqrt(1-x^2))

Lösung

\int \frac{( x + 3 )}{1 - x ^{2}} d x

- 1 - x^{2} + 3 arcsin (x) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 3}{1 - x ^{2}} : \frac{x}{1 - x ^{2}} + \frac{3}{1 - x ^{2}}

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

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

\int \frac{3}{1 - x ^{2}} d x = 3 arcsin (x)

= - 1 - x^{2} + 3 arcsin (x)

Füge eine Konstante zur Lösung hinzu

= - 1 - x^{2} + 3 arcsin (x) + C

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

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