integral from 1 to 3 of x/((x^2+9)^3)

Lösung

\int_{1}^{3} \frac{x}{( x ^{2} + 9 ) ^{3}} d x

\frac{7}{4050}

Dezimale

0.00172 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{x}{( x ^{2} + 9 ) ^{3}} d x

Wende U-Substitution an

= \int_{10}^{18} \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_{10}^{18} \frac{1}{u ^{3}} d u

Wende die Potenzregel an

= \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{10}^{18}

Berechne die Grenzen:

\frac{7}{2025}

= \frac{1}{2} \cdot \frac{7}{2025}

Vereinfache

= \frac{7}{4050}

\int_{0}^{3} x^{2} + 3 d x

\int_{0}^{2 π} - 54 sin^{2} (t) d t

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\int_{0}^{b} 6 e^{x} d x

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