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

Lösung

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

\frac{3}{28}

Dezimale

0.10714 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= 2 \cdot \int_{4}^{7} \frac{1}{2 u ^{2}} 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_{4}^{7} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{u}]_{4}^{7}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{u}]_{4}^{7} : [- \frac{1}{u}]_{4}^{7}

= [- \frac{1}{u}]_{4}^{7}

Berechne die Grenzen:

\frac{3}{28}

= \frac{3}{28}

\int_{- 1}^{3} x^{2} - 2 x + 3 d x

\int_{2}^{5} (x + 5) d x

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

\int_{0}^{1} x^{2} + 2 d x

\int_{0}^{1} x (6 x (1 - x)) d x