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

Lösung

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

\frac{7}{338}

Dezimale

0.02071 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{26} \frac{1}{6 u ^{3}} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{2}^{26} \frac{1}{u ^{3}} d u

Wende die Potenzregel an

= \frac{1}{6} [- \frac{1}{2 u ^{2}}]_{2}^{26}

Berechne die Grenzen:

\frac{21}{169}

= \frac{1}{6} \cdot \frac{21}{169}

Vereinfache

= \frac{7}{338}

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