What is the integral from 0 to 1 of 2+sqrt(2+x^2) ?

The integral from 0 to 1 of 2+sqrt(2+x^2) is 2+(sqrt(3))/2+ln(1/(sqrt(2))+sqrt(3/2))

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integral from 0 to 1 of 2+sqrt(2+x^2)

\int_{0}^{1} 2 + 2 + x^{2} d x

2 + \frac{3}{2} + ln (\frac{1}{2} + \frac{3}{2})

Decimal

3.52450 \dots

Solution steps

\int_{0}^{1} 2 + 2 + x^{2} 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}^{1} 2 d x + \int_{0}^{1} 2 + x^{2} d x

\int_{0}^{1} 2 d x = 2

\int_{0}^{1} 2 + x^{2} d x = \frac{3}{2} + ln (\frac{1}{2} + \frac{3}{2})

= 2 + \frac{3}{2} + ln (\frac{1}{2} + \frac{3}{2})

\int - 40

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What is the integral from 0 to 1 of 2+sqrt(2+x^2) ?
The integral from 0 to 1 of 2+sqrt(2+x^2) is 2+(sqrt(3))/2+ln(1/(sqrt(2))+sqrt(3/2))