integral from 0 to 3 of (2x)/((x^2+2)^3)

Lösung

\int_{0}^{3} \frac{2 x}{( x ^{2} + 2 ) ^{3}} d x

\frac{117}{968}

Dezimale

0.12086 \dots

Schritte zur Lösung

\int_{0}^{3} \frac{2 x}{( x ^{2} + 2 ) ^{3}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{3} \frac{x}{( x ^{2} + 2 ) ^{3}} d x

Wende U-Substitution an

= 2 \cdot \int_{2}^{11} \frac{1}{2 u ^{3}} 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_{2}^{11} \frac{1}{u ^{3}} d u

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{2}^{11}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{2}^{11} : [- \frac{1}{2 u ^{2}}]_{2}^{11}

= [- \frac{1}{2 u ^{2}}]_{2}^{11}

Berechne die Grenzen:

\frac{117}{968}

= \frac{117}{968}

\int_{1}^{3} \frac{5}{t} d t

\int_{0}^{4} x - \frac{x ^{2}}{16} d x

\int_{0}^{4} \frac{1}{4 x - x ^{2}} d x

\int_{0}^{1} x^{4} cos (x^{5}) d x

\int_{0}^{2} 4 x cos (x^{2}) d x