What is the integral from 0 to ln(5) of e^x-e^{-3x} ?

The integral from 0 to ln(5) of e^x-e^{-3x} is 1376/375

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to ln(5) of e^x-e^{-3x}

\int_{0}^{l n (5)} e^{x} - e^{- 3 x} d x

\frac{1376}{375}

Decimal Notation

3.66933 \dots

Solution steps

\int_{0}^{l n (5)} 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 (5)} e^{x} d x - \int_{0}^{l n (5)} e^{- 3 x} d x

\int_{0}^{l n (5)} e^{x} d x = 4

\int_{0}^{l n (5)} e^{- 3 x} d x = \frac{124}{375}

= 4 - \frac{124}{375}

Simplify

4 - \frac{124}{375} : \frac{1376}{375}

= \frac{1376}{375}

\frac{x}{4 x + 6}

\frac{\partial}{\partial x} (x y + \frac{4}{x} + \frac{2}{y})

y = ln (2) (x + 3)

x, 16

y = - 8 e^{- 2 x} - 9 e^{2 x} - 5 e^{x}

What is the integral from 0 to ln(5) of e^x-e^{-3x} ?
The integral from 0 to ln(5) of e^x-e^{-3x} is 1376/375