integral ((6x+3))/((x^2+1))

Lösung

integral

\frac{( 6 x + 3 )}{( x ^{2} + 1 )}

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

Schritte zur Lösung

\int \frac{6 x + 3}{x ^{2} + 1} d x

Multipliziere aus

\frac{6 x + 3}{x ^{2} + 1} : \frac{6 x}{x ^{2} + 1} + \frac{3}{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{6 x}{x ^{2} + 1} d x + \int \frac{3}{x ^{2} + 1} d x

\int \frac{6 x}{x ^{2} + 1} d x = 3 ln x^{2} + 1

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

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

Füge eine Konstante zur Lösung hinzu

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

in t e g r a l \frac{( 1 + a )}{( 1 - a )}

in t e g r a l \frac{1}{cos ^{2} ( 1 - 2 x )}

in t e g r a l \frac{1}{2 x ^{2} y}

in t e g r a l x^{4} e^{x}

in t e g r a l (1 + x)^{\frac{1}{4}}