What is the integral from 0 to ln(6) of e^x-e^{-3x} ?

The integral from 0 to ln(6) of e^x-e^{-3x} is 3025/648

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integral from 0 to ln(6) of e^x-e^{-3x}

\int_{0}^{l n (6)} e^{x} - e^{- 3 x} d x

\frac{3025}{648}

Decimal Notation

4.66820 \dots

Solution steps

\int_{0}^{l n (6)} 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 (6)} e^{x} d x - \int_{0}^{l n (6)} e^{- 3 x} d x

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

\int_{0}^{l n (6)} e^{- 3 x} d x = \frac{215}{648}

= 5 - \frac{215}{648}

Simplify

5 - \frac{215}{648} : \frac{3025}{648}

= \frac{3025}{648}

y = \frac{4 x}{9 - tan ( x )}

arctan (x)

\int_{0}^{1} (x 2 - x^{2}) d x

y = \frac{x}{( 1 + x ^{2} ) , at ( 3 , 0.3 )}

\frac{d}{d x} (1 + 4 sin (x))

What is the integral from 0 to ln(6) of e^x-e^{-3x} ?
The integral from 0 to ln(6) of e^x-e^{-3x} is 3025/648