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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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