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

Lösung

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

\frac{1}{40}

Dezimale

0.025

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{5}^{8} \frac{1}{3 u ^{2}} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{5}^{8} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= \frac{1}{3} [- \frac{1}{u}]_{5}^{8}

Berechne die Grenzen:

\frac{3}{40}

= \frac{1}{3} \cdot \frac{3}{40}

Vereinfache

= \frac{1}{40}

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