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

Lösung

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

\frac{4}{5}

Dezimale

0.8

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= 4 \cdot \int_{2}^{10} \frac{1}{2 u ^{2}} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{2} \cdot \int_{2}^{10} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 4 \cdot \frac{1}{2} [- \frac{1}{u}]_{2}^{10}

Vereinfache

4 \cdot \frac{1}{2} [- \frac{1}{u}]_{2}^{10} : 2 [- \frac{1}{u}]_{2}^{10}

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

Berechne die Grenzen:

\frac{2}{5}

= 2 \cdot \frac{2}{5}

Vereinfache

= \frac{4}{5}

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