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

The integral from 0 to ln(2) of sqrt(e^x)-1 is 2(e^{(ln(2))/2}-1)-ln(2)

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integral from 0 to ln(2) of sqrt(e^x)-1

\int_{0}^{l n (2)} e^{x} - 1 d x

2 (e^{\frac{l n ( 2 )}{2}} - 1) - ln (2)

Decimal

0.13527 \dots

Solution steps

\int_{0}^{l n (2)} e^{x} - 1 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}^{l n (2)} e^{x} d x - \int_{0}^{l n (2)} 1 d x

\int_{0}^{l n (2)} e^{x} d x = 2 (e^{\frac{l n ( 2 )}{2}} - 1)

\int_{0}^{l n (2)} 1 d x = ln (2)

= 2 (e^{\frac{l n ( 2 )}{2}} - 1) - ln (2)

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What is the integral from 0 to ln(2) of sqrt(e^x)-1 ?
The integral from 0 to ln(2) of sqrt(e^x)-1 is 2(e^{(ln(2))/2}-1)-ln(2)