What is the integral from 1 to 3 of ln(x)+sin(x)+8 ?

The integral from 1 to 3 of ln(x)+sin(x)+8 is 3ln(3)+14+cos(1)-cos(3)

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integral from 1 to 3 of ln(x)+sin(x)+8

\int_{1}^{3} ln (x) + sin (x) + 8 d x

3 ln (3) + 14 + cos (1) - cos (3)

Decimal Notation

18.82613 \dots

Solution steps

\int_{1}^{3} 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_{1}^{3} ln (x) d x + \int_{1}^{3} sin (x) d x + \int_{1}^{3} 8 d x

\int_{1}^{3} ln (x) d x = 3 ln (3) - 2

\int_{1}^{3} sin (x) d x = - cos (3) + cos (1)

\int_{1}^{3} 8 d x = 16

= 3 ln (3) - 2 - cos (3) + cos (1) + 16

Simplify

= 3 ln (3) + 14 + cos (1) - cos (3)

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\int_{0}^{3} 4 - 4 x + x^{2} d x

What is the integral from 1 to 3 of ln(x)+sin(x)+8 ?
The integral from 1 to 3 of ln(x)+sin(x)+8 is 3ln(3)+14+cos(1)-cos(3)