integral from 0 to 1 of 1/((2x+1)^2)

Lösung

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

\frac{1}{3}

Dezimale

0.33333 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Wende die Potenzregel an

= \frac{1}{2} [- \frac{1}{u}]_{1}^{3}

Berechne die Grenzen:

\frac{2}{3}

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

Vereinfache

= \frac{1}{3}

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