integral from 0 to 1 of x/((x+31)^2)

Lösung

\int_{0}^{1} \frac{x}{( x + 31 ) ^{2}} d x

5 ln (2) - ln (31) - \frac{1}{32}

Dezimale

0.00049 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x}{( x + 31 ) ^{2}} d x

Wende U-Substitution an

= \int_{31}^{32} \frac{u - 31}{u ^{2}} d u

Multipliziere aus

\frac{u - 31}{u ^{2}} : \frac{1}{u} - \frac{31}{u ^{2}}

= \int_{31}^{32} \frac{1}{u} - \frac{31}{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_{31}^{32} \frac{1}{u} d u - \int_{31}^{32} \frac{31}{u ^{2}} d u

\int_{31}^{32} \frac{1}{u} d u = 5 ln (2) - ln (31)

\int_{31}^{32} \frac{31}{u ^{2}} d u = \frac{1}{32}

= 5 ln (2) - ln (31) - \frac{1}{32}