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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

(x - \frac{a}{x})^{2} : x - 2 a + \frac{a ^{2}}{x}

= \int x - 2 a + \frac{a ^{2}}{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 x d x - \int 2 a d x + \int \frac{a ^{2}}{x} d x

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

\int 2 a d x = 2 a x

\int \frac{a ^{2}}{x} d x = a^{2} ln ∣ x ∣

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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\int 4 sin^{3} (x) cos^{3} (x) d x

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\int \frac{4 x}{( x - 1 ) ( x ^{2} - 1 )} d x

integral of-4/(csc(x))

\int - \frac{4}{csc ( x )} d x

integral of (x-a/x)^2

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

integral of sqrt(36-36cos^2(x))

\int 36 - 36 cos^{2} (x) d x