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Beliebt Rechnen >

integral of (5(x-3)^2)/(xsqrt(x))

Lösung

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

Lösung

5 (\frac{2}{3} x^{\frac{3}{2}} - 12 x - \frac{18}{x}) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Multipliziere aus

\frac{( x - 3 ) ^{2}}{x x} : x - \frac{6}{x} + \frac{9}{x x}

= 5 \cdot \int x - \frac{6}{x} + \frac{9}{x 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

= 5 (\int x d x - \int \frac{6}{x} d x + \int \frac{9}{x x} d x)

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

\int \frac{6}{x} d x = 12 x

\int \frac{9}{x x} d x = - \frac{18}{x}

= 5 (\frac{2}{3} x^{\frac{3}{2}} - 12 x - \frac{18}{x})

Füge eine Konstante zur Lösung hinzu

= 5 (\frac{2}{3} x^{\frac{3}{2}} - 12 x - \frac{18}{x}) + C

Graph

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derivative f(x)= 3/5 x^{15}

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\int_{0}^{2} \frac{y}{25 - y ^{2}} d y

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x \to - \infty lim (\frac{x ^{6} + cos ( x ^{10000} )}{x + 5})

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d er i v a t i v e f (x) = x^{11}

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