integral from 0 to 1 of-1/(x-5)+2/(x-2)

Lösung

\int_{0}^{1} - \frac{1}{x - 5} + \frac{2}{x - 2} d x

- 4 ln (2) + ln (5)

Dezimale

- 1.16315 \dots

Schritte zur Lösung

\int_{0}^{1} - \frac{1}{x - 5} + \frac{2}{x - 2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{0}^{1} \frac{1}{x - 5} d x + \int_{0}^{1} \frac{2}{x - 2} d x

\int_{0}^{1} \frac{1}{x - 5} d x = 2 ln (2) - ln (5)

\int_{0}^{1} \frac{2}{x - 2} d x = - 2 ln (2)

= - (2 ln (2) - ln (5)) - 2 ln (2)

Vereinfache

= - 4 ln (2) + ln (5)

\int (2 x + 6)^{5} d x

d er i v a t i v e 3 cos^{3} (t)

d er i v a t i v e y = e^{x} (3 - 5 x + 3 x^{2})

(1 - y) \cdot e^{y} \cdot y^{^{'}} + \frac{y ^{2}}{x \cdot ln ( x )} = 0

\int \frac{x}{x ^{2} - 7} d x