integral from 2 to 5 of ln(x)+sin(x)+8

解答

\int_{2}^{5} ln (x) + sin (x) + 8 d x

5 ln (5) + 21 + cos (2) - 2 ln (2) - cos (5)

十进制

26.96108 \dots

求解步骤

\int_{2}^{5} ln (x) + sin (x) + 8 d x

使用积分加法定则:

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

= \int_{2}^{5} ln (x) d x + \int_{2}^{5} sin (x) d x + \int_{2}^{5} 8 d x

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

\int_{2}^{5} sin (x) d x = - cos (5) + cos (2)

\int_{2}^{5} 8 d x = 24

= 5 ln (5) - 3 - 2 ln (2) - cos (5) + cos (2) + 24

化简

= 5 ln (5) + 21 + cos (2) - 2 ln (2) - cos (5)

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