What is the integral of (1/2 e^x+3/4 2^x) ?

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

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integral of (1/2 e^x+3/4 2^x)

\int (\frac{1}{2} e^{x} + \frac{3}{4} 2^{x}) d x

\frac{1}{2} e^{x} + \frac{3 \cdot 2 ^{x - 2}}{ln ( 2 )} + C

Solution steps

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

\int \frac{1}{2} e^{x} d x = \frac{1}{2} e^{x}

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

= \frac{1}{2} e^{x} + \frac{3 \cdot 2 ^{x - 2}}{ln ( 2 )}

Add a constant to the solution

= \frac{1}{2} e^{x} + \frac{3 \cdot 2 ^{x - 2}}{ln ( 2 )} + C

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

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