What is the integral from 0 to 1 of 1/2 e^x+3/4 2^x ?

The integral from 0 to 1 of 1/2 e^x+3/4 2^x is (e-1)/2+3/(4ln(2))

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integral from 0 to 1 of 1/2 e^x+3/4 2^x

\int_{0}^{1} \frac{1}{2} e^{x} + \frac{3}{4} 2^{x} d x

\frac{e - 1}{2} + \frac{3}{4 ln ( 2 )}

Decimal

1.94116 \dots

Solution steps

\int_{0}^{1} \frac{1}{2} e^{x} + \frac{3}{4} \cdot 2^{x} 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} \frac{1}{2} e^{x} d x + \int_{0}^{1} \frac{3}{4} \cdot 2^{x} d x

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

\int_{0}^{1} \frac{3}{4} \cdot 2^{x} d x = \frac{3}{4 ln ( 2 )}

= \frac{e - 1}{2} + \frac{3}{4 ln ( 2 )}

What is the integral from 0 to 1 of 1/2 e^x+3/4 2^x ?
The integral from 0 to 1 of 1/2 e^x+3/4 2^x is (e-1)/2+3/(4ln(2))