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Beliebt Rechnen >

integral of (5x+6)/(x^2+1)

Lösung

\int \frac{5 x + 6}{x ^{2} + 1} d x

Lösung

\frac{5}{2} ln x^{2} + 1 + 6 arctan (x) + C

Schritte zur Lösung

\int \frac{5 x + 6}{x ^{2} + 1} d x

Multipliziere aus

\frac{5 x + 6}{x ^{2} + 1} : \frac{5 x}{x ^{2} + 1} + \frac{6}{x ^{2} + 1}

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{5 x}{x ^{2} + 1} d x + \int \frac{6}{x ^{2} + 1} d x

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

\int \frac{6}{x ^{2} + 1} d x = 6 arctan (x)

= \frac{5}{2} ln x^{2} + 1 + 6 arctan (x)

Füge eine Konstante zur Lösung hinzu

= \frac{5}{2} ln x^{2} + 1 + 6 arctan (x) + C

Graph

Beliebte Beispiele

integral of 2*sqrt(x-1)

\int 2 \cdot x - 1 d x

integral of 1/(\sqrt[5]{t^3)}

\int \frac{1}{5 t ^{3}} d t

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

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

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