integral from 3 to 5 of x/((x^2+7)^3)

Lösung

\int_{3}^{5} \frac{x}{( x ^{2} + 7 ) ^{3}} d x

\frac{3}{4096}

Dezimale

0.00073 \dots

Schritte zur Lösung

\int_{3}^{5} \frac{x}{( x ^{2} + 7 ) ^{3}} d x

Wende U-Substitution an

= \int_{16}^{32} \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_{16}^{32} \frac{1}{u ^{3}} d u

Wende die Potenzregel an

= \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{16}^{32}

Berechne die Grenzen:

\frac{3}{2048}

= \frac{1}{2} \cdot \frac{3}{2048}

Vereinfache

= \frac{3}{4096}

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

\int_{0}^{2} sin (2 x) d x

\int_{- 1}^{1} e^{y} d y

\int_{0}^{1} (3 x - 1)^{4} d x

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