integral from 0 to 5 of x^3sqrt(x^2+25)

Lösung

\int_{0}^{5} x^{3} x^{2} + 25 d x

25002 - 625 - \frac{25 ( 250 2 - 125 )}{3}

Dezimale

1005.92231 \dots

Schritte zur Lösung

\int_{0}^{5} x^{3} x^{2} + 25 d x

Wende U-Substitution an

= \int_{5}^{52} (u^{2} - 25) u^{2} d u

Multipliziere aus

(u^{2} - 25) u^{2} : u^{4} - 25 u^{2}

= \int_{5}^{52} u^{4} - 25 u^{2} d u

Wende die Summenregel an:

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

= \int_{5}^{52} u^{4} d u - \int_{5}^{52} 25 u^{2} d u

\int_{5}^{52} u^{4} d u = 25002 - 625

\int_{5}^{52} 25 u^{2} d u = \frac{25 ( 250 2 - 125 )}{3}

= 25002 - 625 - \frac{25 ( 250 2 - 125 )}{3}

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