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Beliebt Rechnen >

integral of (10(x^2+1))/(sqrt(2x+5))

Lösung

\int \frac{10 ( x ^{2} + 1 )}{2 x + 5} d x

Lösung

10 (x^{2} 2 x + 5 - \frac{2}{15} (3 x - 5) (2 x + 5)^{\frac{3}{2}} + 2 x + 5) + C

Schritte zur Lösung

\int \frac{10 ( x ^{2} + 1 )}{2 x + 5} d x

Entferne die Konstante:

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

= 10 \cdot \int \frac{x ^{2} + 1}{2 x + 5} d x

Multipliziere aus

\frac{x ^{2} + 1}{2 x + 5} : \frac{x ^{2}}{2 x + 5} + \frac{1}{2 x + 5}

= 10 \cdot \int \frac{x ^{2}}{2 x + 5} + \frac{1}{2 x + 5} 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

= 10 (\int \frac{x ^{2}}{2 x + 5} d x + \int \frac{1}{2 x + 5} d x)

\int \frac{x ^{2}}{2 x + 5} d x = x^{2} 2 x + 5 - \frac{2}{15} (3 x - 5) (2 x + 5)^{\frac{3}{2}}

\int \frac{1}{2 x + 5} d x = 2 x + 5

= 10 (x^{2} 2 x + 5 - \frac{2}{15} (3 x - 5) (2 x + 5)^{\frac{3}{2}} + 2 x + 5)

Füge eine Konstante zur Lösung hinzu

= 10 (x^{2} 2 x + 5 - \frac{2}{15} (3 x - 5) (2 x + 5)^{\frac{3}{2}} + 2 x + 5) + C

Graph

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