integral from 4 to 5 of (4x^2+x+2)/(x-3)

Lösung

\int_{4}^{5} \frac{4 x ^{2} + x + 2}{x - 3} d x

41 ln (2) + 31

Dezimale

59.41903 \dots

Schritte zur Lösung

\int_{4}^{5} \frac{4 x ^{2} + x + 2}{x - 3} d x

Multipliziere aus

\frac{4 x ^{2} + x + 2}{x - 3} : \frac{4 x ^{2}}{x - 3} + \frac{x}{x - 3} + \frac{2}{x - 3}

Wende die Summenregel an:

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

= \int_{4}^{5} \frac{4 x ^{2}}{x - 3} d x + \int_{4}^{5} \frac{x}{x - 3} d x + \int_{4}^{5} \frac{2}{x - 3} d x

\int_{4}^{5} \frac{4 x ^{2}}{x - 3} d x = 4 (9 ln (2) + \frac{15}{2})

\int_{4}^{5} \frac{x}{x - 3} d x = 1 + 3 ln (2)

\int_{4}^{5} \frac{2}{x - 3} d x = 2 ln (2)

= 4 (9 ln (2) + \frac{15}{2}) + 1 + 3 ln (2) + 2 ln (2)

Vereinfache

4 (9 ln (2) + \frac{15}{2}) + 1 + 3 ln (2) + 2 ln (2) : 41 ln (2) + 31

= 41 ln (2) + 31

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