integral from 0 to 1 of x/((x+15)^2)

Lösung

\int_{0}^{1} \frac{x}{( x + 15 ) ^{2}} d x

4 ln (2) - ln (15) - \frac{1}{16}

Dezimale

0.00203 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x}{( x + 15 ) ^{2}} d x

Wende U-Substitution an

= \int_{15}^{16} \frac{u - 15}{u ^{2}} d u

Multipliziere aus

\frac{u - 15}{u ^{2}} : \frac{1}{u} - \frac{15}{u ^{2}}

= \int_{15}^{16} \frac{1}{u} - \frac{15}{u ^{2}} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{15}^{16} \frac{1}{u} d u - \int_{15}^{16} \frac{15}{u ^{2}} d u

\int_{15}^{16} \frac{1}{u} d u = 4 ln (2) - ln (15)

\int_{15}^{16} \frac{15}{u ^{2}} d u = \frac{1}{16}

= 4 ln (2) - ln (15) - \frac{1}{16}

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