integral of 3/(\sqrt[5]{x^3)}

Lösung

\int \frac{3}{5 x ^{3}} d x

\frac{15}{2} x^{\frac{2}{5}} + C

Schritte zur Lösung

\int \frac{3}{5 x ^{3}} d x

Entferne die Konstante:

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

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

Wende Exponentenregel an:

(a^{n})^{m} = a^{n \cdot m}

5 x^{3} = x^{\frac{3}{5}}

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

Wende die Potenzregel an

= 3 \cdot \frac{5}{2} x^{\frac{2}{5}}

Vereinfache

3 \cdot \frac{5}{2} x^{\frac{2}{5}} : \frac{15}{2} x^{\frac{2}{5}}

= \frac{15}{2} x^{\frac{2}{5}}

Füge eine Konstante zur Lösung hinzu

= \frac{15}{2} x^{\frac{2}{5}} + C

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

x^{2} \frac{d y}{d x} + y = 0

\frac{d}{d x} (sin^{2} (6 x))

\frac{d}{d x} (1 + x - 1)

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