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Beliebt Rechnen >

integral of 4/(x^2+1)-7/x

Lösung

\int \frac{4}{x ^{2} + 1} - \frac{7}{x} d x

Lösung

4 arctan (x) - 7 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{4}{x ^{2} + 1} - \frac{7}{x} d x

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{4}{x ^{2} + 1} d x - \int \frac{7}{x} d x

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

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= 4 arctan (x) - 7 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= 4 arctan (x) - 7 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (6x^3-12x^2+7)/(x^2-2x)

\int \frac{6 x ^{3} - 12 x ^{2} + 7}{x ^{2} - 2 x} d x

integral of y/(sqrt(25-16y^4))

\int \frac{y}{25 - 16 y ^{4}} d y

integral (-3)/x

in t e g r a l \frac{- 3}{x}

integral of 6xsin(3x^2+5)

\int 6 x sin (3 x^{2} + 5) d x

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

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