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

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

Solution steps

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

Expand

\frac{3 - e ^{2 x}}{e ^{x}} : \frac{3}{e ^{x}} - e^{x}

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

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

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

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

Add a constant to the solution

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

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\int_{0}^{1} 6 ln (x) d x

l a pl a ce t r an s f or m 3 t^{2} - 5 e^{3 t}

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