integral from-2 to-1 of x/((x^2+5)^2)

Lösung

\int_{- 2}^{- 1} \frac{x}{( x ^{2} + 5 ) ^{2}} d x

- \frac{1}{36}

Dezimale

- 0.02777 \dots

Schritte zur Lösung

\int_{- 2}^{- 1} \frac{x}{( x ^{2} + 5 ) ^{2}} d x

Wende U-Substitution an

= \int_{9}^{6} \frac{1}{2 u ^{2}} d u

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

= - \int_{6}^{9} \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_{6}^{9} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= - \frac{1}{2} [- \frac{1}{u}]_{6}^{9}

Berechne die Grenzen:

\frac{1}{18}

= - \frac{1}{2} \cdot \frac{1}{18}

Vereinfache

= - \frac{1}{36}

\int_{1}^{e} \frac{( 1 + I n x ) ^{2}}{x} d x

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

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

\int_{- 5}^{6} (36 - x^{2}) - (6 - x) d x

\int_{0}^{6} 4 x^{2} d x