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Beliebt Rechnen >

integral from 0 to 3 of (2t)/((t-4)^2)

Lösung

\int_{0}^{3} \frac{2 t}{( t - 4 ) ^{2}} d t

Lösung

2 (- 2 ln (2) + 3)

+1

Dezimale

3.22741 \dots

Schritte zur Lösung

\int_{0}^{3} \frac{2 t}{( t - 4 ) ^{2}} d t

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{3} \frac{t}{( t - 4 ) ^{2}} d t

Wende U-Substitution an

= 2 \cdot \int_{- 4}^{- 1} \frac{u + 4}{u ^{2}} d u

Multipliziere aus

\frac{u + 4}{u ^{2}} : \frac{1}{u} + \frac{4}{u ^{2}}

= 2 \cdot \int_{- 4}^{- 1} \frac{1}{u} + \frac{4}{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

= 2 (\int_{- 4}^{- 1} \frac{1}{u} d u + \int_{- 4}^{- 1} \frac{4}{u ^{2}} d u)

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

\int_{- 4}^{- 1} \frac{4}{u ^{2}} d u = 3

= 2 (- 2 ln (2) + 3)

Graph

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