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

The integral of 2^x-1-(3x)/2 is (2^x}{ln(2)}-x-\frac{3x^2)/4+C

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integral of 2^x-1-(3x)/2

\int 2^{x} - 1 - \frac{3 x}{2} d x

\frac{2 ^{x}}{ln ( 2 )} - x - \frac{3 x ^{2}}{4} + C

Solution steps

\int 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 2^{x} d x - \int 1 d x - \int \frac{3 x}{2} d x

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

\int 1 d x = x

\int \frac{3 x}{2} d x = \frac{3 x ^{2}}{4}

= \frac{2 ^{x}}{ln ( 2 )} - x - \frac{3 x ^{2}}{4}

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} - x - \frac{3 x ^{2}}{4} + C

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What is the integral of 2^x-1-(3x)/2 ?
The integral of 2^x-1-(3x)/2 is (2^x}{ln(2)}-x-\frac{3x^2)/4+C