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

Lösung

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

16 ln (3) + 20

Dezimale

37.57779 \dots

Schritte zur Lösung

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

Lange Division

\frac{( x + 2 ) ^{2}}{x - 2} : x + 6 + \frac{16}{x - 2}

= \int_{3}^{5} x + 6 + \frac{16}{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_{3}^{5} x d x + \int_{3}^{5} 6 d x + \int_{3}^{5} \frac{16}{x - 2} d x

\int_{3}^{5} x d x = 8

\int_{3}^{5} 6 d x = 12

\int_{3}^{5} \frac{16}{x - 2} d x = 16 ln (3)

= 8 + 12 + 16 ln (3)

Vereinfache

= 16 ln (3) + 20

\int_{4}^{5} \frac{x}{x ^{2} - 5 x + 6} d x

\int_{6}^{\infty} - x e^{- x} d x

\int_{0}^{\frac{1}{2}} cosh (x^{2}) d x

\int_{0}^{π} e^{- x} cos (x) d x

\int_{0}^{2} (x + 1)^{6} d x