What is the integral from 1 to 9 of (4/x-e^{-x}) ?

The integral from 1 to 9 of (4/x-e^{-x}) is 8ln(3)-1/e+1/(e^9)

Popular >

integral from 1 to 9 of (4/x-e^{-x})

\int_{1}^{9} (\frac{4}{x} - e^{- x}) d x

8 ln (3) - \frac{1}{e} + \frac{1}{e ^{9}}

Decimal

8.42114 \dots

Solution steps

\int_{1}^{9} \frac{4}{x} - e^{- 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_{1}^{9} \frac{4}{x} d x - \int_{1}^{9} e^{- x} d x

\int_{1}^{9} \frac{4}{x} d x = 8 ln (3)

\int_{1}^{9} e^{- x} d x = \frac{1}{e} - \frac{1}{e ^{9}}

= 8 ln (3) - (\frac{1}{e} - \frac{1}{e ^{9}})

Simplify

= 8 ln (3) - \frac{1}{e} + \frac{1}{e ^{9}}

\int_{1}^{e} \frac{( x ^{5} + 1 )}{x} d x

\int_{0}^{\frac{1}{2}} x^{2} e^{2 x} d x

\int_{1}^{\infty} \frac{1}{n}

\int_{0}^{4} 8 x - 5 d x

\int_{0}^{π} cos^{2} (n x) d x

What is the integral from 1 to 9 of (4/x-e^{-x}) ?
The integral from 1 to 9 of (4/x-e^{-x}) is 8ln(3)-1/e+1/(e^9)