integral from 1 to 4 of (x+1)(x^2+2x)^2

Lösung

\int_{1}^{4} (x + 1) (x^{2} + 2 x)^{2} d x

\frac{4599}{2}

Dezimale

2299.5

Schritte zur Lösung

\int_{1}^{4} (x + 1) (x^{2} + 2 x)^{2} d x

Wende U-Substitution an

= \int_{3}^{24} \frac{u ^{2}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{3}^{24} u^{2} d u

Wende die Potenzregel an

= \frac{1}{2} [\frac{u ^{3}}{3}]_{3}^{24}

Berechne die Grenzen:

4599

= \frac{1}{2} \cdot 4599

Vereinfache

= \frac{4599}{2}

\int_{1}^{e} \frac{8 ln ( x )}{x} d x

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