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Beliebt Rechnen >

integral of (3+9x)/(1+x^2)

Lösung

\int \frac{3 + 9 x}{1 + x ^{2}} d x

Lösung

3 arctan (x) + \frac{9}{2} ln 1 + x^{2} + C

Schritte zur Lösung

\int \frac{3 + 9 x}{1 + x ^{2}} d x

Multipliziere aus

\frac{3 + 9 x}{1 + x ^{2}} : \frac{3}{1 + x ^{2}} + \frac{9 x}{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{3}{1 + x ^{2}} d x + \int \frac{9 x}{1 + x ^{2}} d x

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

\int \frac{9 x}{1 + x ^{2}} d x = \frac{9}{2} ln 1 + x^{2}

= 3 arctan (x) + \frac{9}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= 3 arctan (x) + \frac{9}{2} ln 1 + x^{2} + C

Graph

Beliebte Beispiele

integral of (x^2+x+9)sqrt(x+8)

\int (x^{2} + x + 9) x + 8 d x

integral of (x^4)/((2+x^5)^6)

\int \frac{x ^{4}}{( 2 + x ^{5} ) ^{6}} d x

integral of (3x-4)(2x+3)

\int (3 x - 4) (2 x + 3) d x

integral of (x^2-x+3)

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

integral of (x^2+4)(sqrt(x)-4)

\int (x^{2} + 4) (x - 4) d x