What is the integral of (e^{8x}(e^{-6x}))/(-15e^x) ?

The integral of (e^{8x}(e^{-6x}))/(-15e^x) is -1/15 e^x+C

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integral of (e^{8x}(e^{-6x}))/(-15e^x)

\int \frac{e ^{8 x} ( e ^{- 6 x} )}{- 15 e ^{x}} d x

- \frac{1}{15} e^{x} + C

Solution steps

\int \frac{e ^{8 x} e ^{- 6 x}}{- 15 e ^{x}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{- 15} \cdot \int \frac{e ^{8 x} e ^{- 6 x}}{e ^{x}} d x

Simplify

= (- \frac{1}{15}) \cdot \int \frac{e ^{8 x} e ^{- 6 x}}{e ^{x}} d x

Simplify

\frac{e ^{8 x} e ^{- 6 x}}{e ^{x}} : e^{x}

= (- \frac{1}{15}) \cdot \int e^{x} d x

Use the common integral:

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

= (- \frac{1}{15}) e^{x}

Simplify

= - \frac{1}{15} e^{x}

Add a constant to the solution

= - \frac{1}{15} e^{x} + C

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What is the integral of (e^{8x}(e^{-6x}))/(-15e^x) ?
The integral of (e^{8x}(e^{-6x}))/(-15e^x) is -1/15 e^x+C