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Beliebt Rechnen >

integral of 5/(x^3)+5/(x^2)+5/x

Lösung

\int \frac{5}{x ^{3}} + \frac{5}{x ^{2}} + \frac{5}{x} d x

Lösung

- \frac{5}{2 x ^{2}} - \frac{5}{x} + 5 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{5}{x ^{3}} + \frac{5}{x ^{2}} + \frac{5}{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{5}{x ^{3}} d x + \int \frac{5}{x ^{2}} d x + \int \frac{5}{x} d x

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}}

\int \frac{5}{x ^{2}} d x = - \frac{5}{x}

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= - \frac{5}{2 x ^{2}} - \frac{5}{x} + 5 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{5}{2 x ^{2}} - \frac{5}{x} + 5 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

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

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

integral of (5x)/(x^2+3)

\int \frac{5 x}{x ^{2} + 3} d x

integral of x/(sqrt(16-4x^2))

\int \frac{x}{16 - 4 x ^{2}} d x

integral of 1/(4x^7)

\int \frac{1}{4 x ^{7}} d x

integral of (9^x)

\int (9^{x}) d x