integral from 0 to 1 of x/((x^2+3)^3)

Lösung

\int_{0}^{1} \frac{x}{( x ^{2} + 3 ) ^{3}} d x

\frac{7}{576}

Dezimale

0.01215 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x}{( x ^{2} + 3 ) ^{3}} d x

Wende U-Substitution an

= \int_{3}^{4} \frac{1}{2 u ^{3}} 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}^{4} \frac{1}{u ^{3}} d u

Wende die Potenzregel an

= \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{3}^{4}

Berechne die Grenzen:

\frac{7}{288}

= \frac{1}{2} \cdot \frac{7}{288}

Vereinfache

= \frac{7}{576}

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