integral from 2 to 5 of x^{1/3}(-1-2x)

Lösung

\int_{2}^{5} x^{\frac{1}{3}} (- 1 - 2 x) d x

\frac{276 - 705 \cdot 2 ^{\frac{2}{3}} \cdot 5 ^{\frac{1}{3}}}{28 \cdot 2 ^{\frac{2}{3}}}

Dezimale

- 36.84514 \dots

Schritte zur Lösung

\int_{2}^{5} x^{\frac{1}{3}} (- 1 - 2 x) d x

Multipliziere aus

x^{\frac{1}{3}} (- 1 - 2 x) : - x^{\frac{1}{3}} - 2 x^{\frac{4}{3}}

= \int_{2}^{5} - x^{\frac{1}{3}} - 2 x^{\frac{4}{3}} d x

Wende die Summenregel an:

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

= - \int_{2}^{5} x^{\frac{1}{3}} d x - \int_{2}^{5} 2 x^{\frac{4}{3}} d x

\int_{2}^{5} x^{\frac{1}{3}} d x = \frac{15 \cdot 5 ^{\frac{1}{3}}}{4} - \frac{3}{2 ^{\frac{2}{3}}}

\int_{2}^{5} 2 x^{\frac{4}{3}} d x = \frac{2 ( 75 \cdot 5 ^{\frac{1}{3}} - 12 \cdot 2 ^{\frac{1}{3}} )}{7}

= - (\frac{15 \cdot 5 ^{\frac{1}{3}}}{4} - \frac{3}{2 ^{\frac{2}{3}}}) - \frac{2 ( 75 \cdot 5 ^{\frac{1}{3}} - 12 \cdot 2 ^{\frac{1}{3}} )}{7}

Vereinfache

- (\frac{15 \cdot 5 ^{\frac{1}{3}}}{4} - \frac{3}{2 ^{\frac{2}{3}}}) - \frac{2 ( 75 \cdot 5 ^{\frac{1}{3}} - 12 \cdot 2 ^{\frac{1}{3}} )}{7} : \frac{276 - 705 \cdot 2 ^{\frac{2}{3}} \cdot 5 ^{\frac{1}{3}}}{28 \cdot 2 ^{\frac{2}{3}}}

= \frac{276 - 705 \cdot 2 ^{\frac{2}{3}} \cdot 5 ^{\frac{1}{3}}}{28 \cdot 2 ^{\frac{2}{3}}}

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