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

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

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

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

- \frac{3 + e ^{2 x}}{e ^{x}} + 2 e^{x} + C

Solution steps

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

Apply Integration By Parts

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

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

\int - 2 e^{x} d x = - 2 e^{x}

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

Simplify

= - \frac{3 + e ^{2 x}}{e ^{x}} + 2 e^{x}

Add a constant to the solution

= - \frac{3 + e ^{2 x}}{e ^{x}} + 2 e^{x} + C

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