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Beliebt Rechnen >

integral from 0 to 5 of (5t)/((t-6)^2)

Lösung

\int_{0}^{5} \frac{5 t}{( t - 6 ) ^{2}} d t

Lösung

5 (- ln (6) + 5)

+1

Dezimale

16.04120 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{5 t}{( t - 6 ) ^{2}} d t

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{5} \frac{t}{( t - 6 ) ^{2}} d t

Wende U-Substitution an

= 5 \cdot \int_{- 6}^{- 1} \frac{u + 6}{u ^{2}} d u

Multipliziere aus

\frac{u + 6}{u ^{2}} : \frac{1}{u} + \frac{6}{u ^{2}}

= 5 \cdot \int_{- 6}^{- 1} \frac{1}{u} + \frac{6}{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

= 5 (\int_{- 6}^{- 1} \frac{1}{u} d u + \int_{- 6}^{- 1} \frac{6}{u ^{2}} d u)

\int_{- 6}^{- 1} \frac{1}{u} d u = - ln (6)

\int_{- 6}^{- 1} \frac{6}{u ^{2}} d u = 5

= 5 (- ln (6) + 5)

Graph

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(dy)/(dx)=y(2x-5)

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