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Beliebt Rechnen >

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

Lösung

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

Lösung

2 1 + x^{2} + 3 ln x^{2} + 1 + x + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= 2 1 + x^{2} + 3 ln x^{2} + 1 + x

Füge eine Konstante zur Lösung hinzu

= 2 1 + x^{2} + 3 ln x^{2} + 1 + x + C

Graph

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