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Beliebt Rechnen >

integral of x/(\sqrt[4]{x+9)}

Lösung

\int \frac{x}{4 x + 9} d x

Lösung

\frac{4}{7} (x + 9)^{\frac{7}{4}} - 12 (x + 9)^{\frac{3}{4}} + C

Schritte zur Lösung

\int \frac{x}{4 x + 9} d x

Wende U-Substitution an

= \int \frac{u - 9}{4 u} d u

Multipliziere aus

\frac{u - 9}{4 u} : u^{\frac{3}{4}} - \frac{9}{4 u}

= \int u^{\frac{3}{4}} - \frac{9}{4 u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{\frac{3}{4}} d u - \int \frac{9}{4 u} d u

\int u^{\frac{3}{4}} d u = \frac{4}{7} u^{\frac{7}{4}}

\int \frac{9}{4 u} d u = 12 u^{\frac{3}{4}}

= \frac{4}{7} u^{\frac{7}{4}} - 12 u^{\frac{3}{4}}

Setze in

u = x + 9

ein

= \frac{4}{7} (x + 9)^{\frac{7}{4}} - 12 (x + 9)^{\frac{3}{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{7} (x + 9)^{\frac{7}{4}} - 12 (x + 9)^{\frac{3}{4}} + C

Graph

Beliebte Beispiele

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

integral from 1 to 2 of (x^2+1)/(x^2)

\int_{1}^{2} \frac{x ^{2} + 1}{x ^{2}} d x

derivative x\sqrt[3]{x}

d er i v a t i v e x 3 x

integral from 0 to 4 of x^2-4x

\int_{0}^{4} x^{2} - 4 x d x

derivative 1/(t+1)

d er i v a t i v e \frac{1}{t + 1}