integral from 1 to 2 of 5x(x^2+1)

Lösung

\int_{1}^{2} 5 x (x^{2} + 1) d x

\frac{105}{4}

Dezimale

26.25

Schritte zur Lösung

\int_{1}^{2} 5 x (x^{2} + 1) d x

Entferne die Konstante:

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

= 5 \cdot \int_{1}^{2} x (x^{2} + 1) d x

Multipliziere aus

x (x^{2} + 1) : x^{3} + x

= 5 \cdot \int_{1}^{2} x^{3} + x 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

= 5 (\int_{1}^{2} x^{3} d x + \int_{1}^{2} x d x)

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

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

= 5 (\frac{15}{4} + \frac{3}{2})

Vereinfache

5 (\frac{15}{4} + \frac{3}{2}) : \frac{105}{4}

= \frac{105}{4}

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