What is the integral from 0 to 2 of (2^x-1-(3x)/2) ?

The integral from 0 to 2 of (2^x-1-(3x)/2) is 3/(ln(2))-5

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integral from 0 to 2 of (2^x-1-(3x)/2)

\int_{0}^{2} (2^{x} - 1 - \frac{3 x}{2}) d x

\frac{3}{ln ( 2 )} - 5

Decimal Notation

- 0.67191 \dots

Solution steps

\int_{0}^{2} 2^{x} - 1 - \frac{3 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}^{2} 2^{x} d x - \int_{0}^{2} 1 d x - \int_{0}^{2} \frac{3 x}{2} d x

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

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

\int_{0}^{2} \frac{3 x}{2} d x = 3

= \frac{3}{ln ( 2 )} - 2 - 3

Simplify

= \frac{3}{ln ( 2 )} - 5

\int_{0}^{1} ln^{3} (x) d x

\int_{0}^{3} (3 x - 5) d x

\int_{1}^{4} 2^{4 x} d x

\int_{0}^{\frac{1}{x y}} ln (y) d y

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

What is the integral from 0 to 2 of (2^x-1-(3x)/2) ?
The integral from 0 to 2 of (2^x-1-(3x)/2) is 3/(ln(2))-5