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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (25x^2-10x+1)

\int (25 x^{2} - 10 x + 1) d x

integral of (2x^2+3x+18)/((2x+1)(x^2+4))

\int \frac{2 x ^{2} + 3 x + 18}{( 2 x + 1 ) ( x ^{2} + 4 )} d x

integral of-2x-3

\int - 2 x - 3 d x

integral of ((sqrt(x^2-1))/x)

\int (\frac{x ^{2} - 1}{x}) d x

integral of (4x^2+3x+6)/(x^2(x^2+3))

\int \frac{4 x ^{2} + 3 x + 6}{x ^{2} ( x ^{2} + 3 )} d x