What is the integral from 0 to ln(3) of e^x-e^{-2x} ?

The integral from 0 to ln(3) of e^x-e^{-2x} is 14/9

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integral from 0 to ln(3) of e^x-e^{-2x}

\int_{0}^{l n (3)} e^{x} - e^{- 2 x} d x

\frac{14}{9}

Decimal Notation

1.55555 \dots

Solution steps

\int_{0}^{l n (3)} 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 (3)} e^{x} d x - \int_{0}^{l n (3)} e^{- 2 x} d x

\int_{0}^{l n (3)} e^{x} d x = 2

\int_{0}^{l n (3)} e^{- 2 x} d x = \frac{4}{9}

= 2 - \frac{4}{9}

Simplify

2 - \frac{4}{9} : \frac{14}{9}

= \frac{14}{9}

\frac{d y}{d x} + \frac{2}{x} y = 6 x^{4} y^{2}

\frac{d y}{d x} = \frac{y}{x + 2 y}

4 e^{x + 4} + 1

x \to \infty + lim (f (x))

f (x) =, x

What is the integral from 0 to ln(3) of e^x-e^{-2x} ?
The integral from 0 to ln(3) of e^x-e^{-2x} is 14/9