integral of (1+4x)^{3/5}

Lösung

\int (1 + 4 x)^{\frac{3}{5}} d x

\frac{5}{32} (1 + 4 x)^{\frac{8}{5}} + C

Schritte zur Lösung

\int (1 + 4 x)^{\frac{3}{5}} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int u^{\frac{3}{5}} d u

Wende die Potenzregel an

= \frac{1}{4} \cdot \frac{5}{8} u^{\frac{8}{5}}

Setze in

u = 1 + 4 x

ein

= \frac{1}{4} \cdot \frac{5}{8} (1 + 4 x)^{\frac{8}{5}}

Vereinfache

\frac{1}{4} \cdot \frac{5}{8} (1 + 4 x)^{\frac{8}{5}} : \frac{5}{32} (1 + 4 x)^{\frac{8}{5}}

= \frac{5}{32} (1 + 4 x)^{\frac{8}{5}}

Füge eine Konstante zur Lösung hinzu

= \frac{5}{32} (1 + 4 x)^{\frac{8}{5}} + C

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