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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

\frac{2 x + 3}{x ^{2} + 9} : \frac{2 x}{x ^{2} + 9} + \frac{3}{x ^{2} + 9}

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

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

\int \frac{3}{x ^{2} + 9} d x = arctan (\frac{x}{3})

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of (ln(x^2-3)^3)

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

implicit (dy)/(dx),x^2+y^2=4

im pl i c i t \frac{d y}{d x}, x^{2} + y^{2} = 4

derivative y=log_{3}(8x-1)

d er i v a t i v e y = lo g_{3} (8 x - 1)

(d^2)/(dx^2)(sqrt(1+x^2))

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

y^'+y/(6960)=0.0025862069

y^{^{'}} + \frac{y}{6960} = 0.0025862069