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Beliebt Rechnen >

integral of (3x+4)/(1+x^2)

Lösung

\int \frac{3 x + 4}{1 + x ^{2}} d x

Lösung

\frac{3}{2} ln 1 + x^{2} + 4 arctan (x) + C

Schritte zur Lösung

\int \frac{3 x + 4}{1 + x ^{2}} d x

Multipliziere aus

\frac{3 x + 4}{1 + x ^{2}} : \frac{3 x}{1 + x ^{2}} + \frac{4}{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 x}{1 + x ^{2}} d x + \int \frac{4}{1 + x ^{2}} d x

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

\int \frac{4}{1 + x ^{2}} d x = 4 arctan (x)

= \frac{3}{2} ln 1 + x^{2} + 4 arctan (x)

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} ln 1 + x^{2} + 4 arctan (x) + C

Graph

Beliebte Beispiele

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

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

integral of (cos(x))/(sin(x)+3)

\int \frac{cos ( x )}{sin ( x ) + 3} d x

integral of (1/(x+5))

\int (\frac{1}{x + 5}) d x

integral of 9/(1+t^2)

\int \frac{9}{1 + t ^{2}} d t

integral of 1/(xln(x^{15))}

\int \frac{1}{x ln ( x ^{15} )} d x