What is the integral from 2 to 5 of ln(x)+sin(x)+8 ?

The integral from 2 to 5 of ln(x)+sin(x)+8 is 5ln(5)+21+cos(2)-2ln(2)-cos(5)

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

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

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

Solution steps

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

Simplify

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

\int_{\frac{y}{n}}^{1} n (1 - x)^{n - 1} d x

\int_{1}^{3} (x^{2} - 8 x + 15) d x

\int_{0}^{5} - 4 x d x

\int_{0}^{x} \frac{e ^{2 s} - 1}{s} d s

What is the integral from 2 to 5 of ln(x)+sin(x)+8 ?
The integral from 2 to 5 of ln(x)+sin(x)+8 is 5ln(5)+21+cos(2)-2ln(2)-cos(5)