What is the integral from 0.5 to 1 of ln(x)+x ?

The integral from 0.5 to 1 of ln(x)+x is 0.22157…

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integral from 0.5 to 1 of ln(x)+x

\int_{0.5}^{1} ln (x) + x d x

0.22157 \dots

Solution steps

\int_{0.5}^{1} ln (x) + x d x

Apply the Sum Rule:

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

= \int_{0.5}^{1} ln (x) d x + \int_{0.5}^{1} x d x

\int_{0.5}^{1} ln (x) d x = - 0.15342 \dots

\int_{0.5}^{1} x d x = 0.375

= - 0.15342 \dots + 0.375

Simplify

= 0.22157 \dots

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What is the integral from 0.5 to 1 of ln(x)+x ?
The integral from 0.5 to 1 of ln(x)+x is 0.22157…