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Beliebt Rechnen >

integral from-1 to 2 of 2/((2x+4)^3)

Lösung

\int_{- 1}^{2} \frac{2}{( 2 x + 4 ) ^{3}} d x

Lösung

\frac{15}{128}

+1

Dezimale

0.1171875

Schritte zur Lösung

\int_{- 1}^{2} \frac{2}{( 2 x + 4 ) ^{3}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{- 1}^{2} \frac{1}{( 2 x + 4 ) ^{3}} d x

Wende U-Substitution an

= 2 \cdot \int_{2}^{8} \frac{1}{2 u ^{3}} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{2} \cdot \int_{2}^{8} \frac{1}{u ^{3}} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{2}^{8}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{2}^{8} : [- \frac{1}{2 u ^{2}}]_{2}^{8}

= [- \frac{1}{2 u ^{2}}]_{2}^{8}

Berechne die Grenzen:

\frac{15}{128}

= \frac{15}{128}

Graph

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