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Beliebt Rechnen >

integral of x/(\sqrt[4]{x+5)}

Lösung

\int \frac{x}{4 x + 5} d x

Lösung

\frac{4}{7} (x + 5)^{\frac{7}{4}} - \frac{20}{3} (x + 5)^{\frac{3}{4}} + C

Schritte zur Lösung

\int \frac{x}{4 x + 5} d x

Wende U-Substitution an

= \int \frac{u - 5}{4 u} d u

Multipliziere aus

\frac{u - 5}{4 u} : u^{\frac{3}{4}} - \frac{5}{4 u}

= \int u^{\frac{3}{4}} - \frac{5}{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{5}{4 u} d u

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

\int \frac{5}{4 u} d u = \frac{20}{3} u^{\frac{3}{4}}

= \frac{4}{7} u^{\frac{7}{4}} - \frac{20}{3} u^{\frac{3}{4}}

Setze in

u = x + 5

ein

= \frac{4}{7} (x + 5)^{\frac{7}{4}} - \frac{20}{3} (x + 5)^{\frac{3}{4}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{7} (x + 5)^{\frac{7}{4}} - \frac{20}{3} (x + 5)^{\frac{3}{4}} + C

Graph

Beliebte Beispiele

integral of 1/(3x^2+5x+1)

\int \frac{1}{3 x ^{2} + 5 x + 1} d x

integral of 1/(sqrt(e^{2x)-25)}

\int \frac{1}{e ^{2 x} - 25} d x

integral of (-1)/(x(ln(x))^3)

\int \frac{- 1}{x ( ln ( x ) ) ^{3}} d x

integral of (sqrt(arctan(x)))/(1+x^2)

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

integral of x(3x^2+2)^8

\int x (3 x^{2} + 2)^{8} d x