What is the integral from 0 to ln(4) of e^x-e^{-3x} ?

The integral from 0 to ln(4) of e^x-e^{-3x} is 171/64

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integral from 0 to ln(4) of e^x-e^{-3x}

\int_{0}^{l n (4)} e^{x} - e^{- 3 x} d x

\frac{171}{64}

Decimal

2.671875

Solution steps

\int_{0}^{l n (4)} e^{x} - e^{- 3 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 (4)} e^{x} d x - \int_{0}^{l n (4)} e^{- 3 x} d x

\int_{0}^{l n (4)} e^{x} d x = 3

\int_{0}^{l n (4)} e^{- 3 x} d x = \frac{21}{64}

= 3 - \frac{21}{64}

Simplify

3 - \frac{21}{64} : \frac{171}{64}

= \frac{171}{64}

What is the integral from 0 to ln(4) of e^x-e^{-3x} ?
The integral from 0 to ln(4) of e^x-e^{-3x} is 171/64