integral from 0 to 5 of (7t)/((t-6)^2)

Lösung

\int_{0}^{5} \frac{7 t}{( t - 6 ) ^{2}} d t

7 (- ln (6) + 5)

Dezimale

22.45768 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{7 t}{( t - 6 ) ^{2}} d t

Entferne die Konstante:

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

= 7 \cdot \int_{0}^{5} \frac{t}{( t - 6 ) ^{2}} d t

Wende U-Substitution an

= 7 \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}}

= 7 \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

= 7 (\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

= 7 (- ln (6) + 5)

t an g e n t f (x) = \frac{1}{x ^{3}}, (- 3, - \frac{1}{27})

\int \frac{t ^{2}}{( t ^{3} - 2 ) ^{5}} d t

n = 1 \sum \infty (1 - \frac{1}{3 n})^{n}

x \to - 3 lim (\frac{x ^{2} - 6}{3 - x})

y^{^{''}} - 6 y^{^{'}} + 36 y = 0