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

Lösung

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

\frac{1}{( x + 2 ) ( x + 1 )}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{x + 1}^{x + 2} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

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

Berechne die Grenzen:

- \frac{1}{x + 2} + \frac{1}{x + 1}

= - \frac{1}{x + 2} + \frac{1}{x + 1}

Vereinfache

= \frac{1}{( x + 2 ) ( x + 1 )}

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