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Beliebt Rechnen >

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

Lösung

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

Lösung

2 (- ln (6) + 5)

+1

Dezimale

6.41648 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= 2 \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}}

= 2 \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

= 2 (\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

= 2 (- ln (6) + 5)

Graph

Beliebte Beispiele

integral of (x+2)/(x^2+6x+10)

\int \frac{x + 2}{x ^{2} + 6 x + 10} d x

xy^'+3y=((e^x))/x

x y^{^{'}} + 3 y = \frac{( e ^{x} )}{x}

(\partial)/(\partial y)(5xsin(y))

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integral of x^{-3}

\int x^{- 3} d x