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Beliebt Rechnen >

integral of 1/x (\sqrt[6]{x^5})

Lösung

\int \frac{1}{x} (6 x^{5}) d x

Lösung

\frac{6}{5} x^{\frac{5}{6}} + C

Schritte zur Lösung

\int \frac{1}{x} 6 x^{5} d x

6 x^{5} = x^{\frac{5}{6}},

angenommen

x \geq 0

= \int \frac{1}{x} x^{\frac{5}{6}} d x

Vereinfache

\frac{1}{x} x^{\frac{5}{6}} : \frac{1}{x ^{\frac{1}{6}}}

= \int \frac{1}{x ^{\frac{1}{6}}} d x

Wende die Potenzregel an

= \frac{6}{5} x^{\frac{5}{6}}

Füge eine Konstante zur Lösung hinzu

= \frac{6}{5} x^{\frac{5}{6}} + C

Graph

Beliebte Beispiele

integral of sqrt(1+5x^2)

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

integral of (3x+2)/((x-4)(x+2))

\int \frac{3 x + 2}{( x - 4 ) ( x + 2 )} d x

integral of (5x+1)(2x-2)

\int (5 x + 1) (2 x - 2) d x

integral of (2x^2-5x-7)/(x-3)

\int \frac{2 x ^{2} - 5 x - 7}{x - 3} d x

integral of (6x)/(e^{3x)}

\int \frac{6 x}{e ^{3 x}} d x