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

Lösung

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

- \frac{3}{56}

Dezimale

- 0.05357 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{3}{28}

= - \frac{1}{2} \cdot \frac{3}{28}

Vereinfache

= - \frac{3}{56}

\int_{0}^{1} y^{2} 1 - y^{2} d y

\int_{1}^{3} ∣ x ∣ - 1 d x

\int_{- 5}^{5} \frac{4}{x ^{3}} d x

\int_{1}^{3} x^{3} e^{x} d x

\int_{0}^{1} 3 t^{3} d t