integral from 4 to 6 of x/(x-3)

Lösung

\int_{4}^{6} \frac{x}{x - 3} d x

2 + 3 ln (3)

Dezimale

5.29583 \dots

Schritte zur Lösung

\int_{4}^{6} \frac{x}{x - 3} d x

Wende U-Substitution an

= \int_{1}^{3} \frac{u + 3}{u} d u

Multipliziere aus

\frac{u + 3}{u} : 1 + \frac{3}{u}

= \int_{1}^{3} 1 + \frac{3}{u} 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_{1}^{3} 1 d u + \int_{1}^{3} \frac{3}{u} d u

\int_{1}^{3} 1 d u = 2

\int_{1}^{3} \frac{3}{u} d u = 3 ln (3)

= 2 + 3 ln (3)

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

\int_{e^{3}}^{e^{6}} ln (x) d x

\int_{1}^{4} x + \frac{1}{x} d x

\int_{- \infty}^{0} x e^{a x} d x

\int_{0}^{π} x^{3} cos (2 x) d x