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Beliebt Rechnen >

integral of ((7x+3))/(1+x^2)

Lösung

\int \frac{( 7 x + 3 )}{1 + x ^{2}} d x

Lösung

\frac{7}{2} ln 1 + x^{2} + 3 arctan (x) + C

Schritte zur Lösung

\int \frac{7 x + 3}{1 + x ^{2}} d x

Multipliziere aus

\frac{7 x + 3}{1 + x ^{2}} : \frac{7 x}{1 + x ^{2}} + \frac{3}{1 + x ^{2}}

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

\int \frac{7 x}{1 + x ^{2}} d x = \frac{7}{2} ln 1 + x^{2}

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

= \frac{7}{2} ln 1 + x^{2} + 3 arctan (x)

Füge eine Konstante zur Lösung hinzu

= \frac{7}{2} ln 1 + x^{2} + 3 arctan (x) + C

Graph

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