What is the integral from 0 to ln(6) of e^x-e^{-2x} ?

The integral from 0 to ln(6) of e^x-e^{-2x} is 325/72

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integral from 0 to ln(6) of e^x-e^{-2x}

\int_{0}^{l n (6)} e^{x} - e^{- 2 x} d x

\frac{325}{72}

Decimal Notation

4.51388 \dots

Solution steps

\int_{0}^{l n (6)} e^{x} - e^{- 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_{0}^{l n (6)} e^{x} d x - \int_{0}^{l n (6)} e^{- 2 x} d x

\int_{0}^{l n (6)} e^{x} d x = 5

\int_{0}^{l n (6)} e^{- 2 x} d x = \frac{35}{72}

= 5 - \frac{35}{72}

Simplify

5 - \frac{35}{72} : \frac{325}{72}

= \frac{325}{72}

\int x - 2 d x

\int 6 sin^{3} (x) cos^{2} (x) d x

\int x cos^{2} (x) sin (x) d x

f (x) = x^{2} - 1, (- 2, 3)

x \to 2 lim (\frac{3}{2 - x})

What is the integral from 0 to ln(6) of e^x-e^{-2x} ?
The integral from 0 to ln(6) of e^x-e^{-2x} is 325/72