integral from 1 to 6 of x^2sqrt(x+3)

Lösung

\int_{1}^{6} x^{2} x + 3 d x

\frac{6856}{35}

Dezimale

195.88571 \dots

Schritte zur Lösung

\int_{1}^{6} x^{2} x + 3 d x

Wende U-Substitution an

= \int_{4}^{9} (u - 3)^{2} u d u

Multipliziere aus

(u - 3)^{2} u : u^{\frac{5}{2}} - 6 u^{\frac{3}{2}} + 9 u

= \int_{4}^{9} u^{\frac{5}{2}} - 6 u^{\frac{3}{2}} + 9 u 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_{4}^{9} u^{\frac{5}{2}} d u - \int_{4}^{9} 6 u^{\frac{3}{2}} d u + \int_{4}^{9} 9 u d u

\int_{4}^{9} u^{\frac{5}{2}} d u = \frac{4118}{7}

\int_{4}^{9} 6 u^{\frac{3}{2}} d u = \frac{2532}{5}

\int_{4}^{9} 9 u d u = 114

= \frac{4118}{7} - \frac{2532}{5} + 114

Vereinfache

\frac{4118}{7} - \frac{2532}{5} + 114 : \frac{6856}{35}

= \frac{6856}{35}

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