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Beliebt Rechnen >

integral of (2+5x)/(1+x^2)

Lösung

\int \frac{2 + 5 x}{1 + x ^{2}} d x

Lösung

2 arctan (x) + \frac{5}{2} ln 1 + x^{2} + C

Schritte zur Lösung

\int \frac{2 + 5 x}{1 + x ^{2}} d x

Multipliziere aus

\frac{2 + 5 x}{1 + x ^{2}} : \frac{2}{1 + x ^{2}} + \frac{5 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{2}{1 + x ^{2}} d x + \int \frac{5 x}{1 + x ^{2}} d x

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

\int \frac{5 x}{1 + x ^{2}} d x = \frac{5}{2} ln 1 + x^{2}

= 2 arctan (x) + \frac{5}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= 2 arctan (x) + \frac{5}{2} ln 1 + x^{2} + C

Graph

Beliebte Beispiele

derivative of (-5x^{30})

\frac{d}{d x} ((- 5 x)^{30})

integral from-4 to 5 of 8-y-((y-2)^2)/3

\int_{- 4}^{5} 8 - y - \frac{( y - 2 ) ^{2}}{3} d y

derivative of Cx+C-C^2

\frac{d}{d x} (C x + C - C^{2})

x^3y^{'''}-2x^2y^{''}+13xy^'-13y=0

x^{3} y^{^{'''}} - 2 x^{2} y^{^{''}} + 13 x y^{^{'}} - 13 y = 0

fläche y= 3/x ,y= 3/(x^2),x=5

a re a y = \frac{3}{x}, y = \frac{3}{x ^{2}}, x = 5