What is the integral from 1 to 5 of (3x^{-1}+x^{-3}) ?

The integral from 1 to 5 of (3x^{-1}+x^{-3}) is 3ln(5)+12/25

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integral from 1 to 5 of (3x^{-1}+x^{-3})

\int_{1}^{5} (3 x^{- 1} + x^{- 3}) d x

3 ln (5) + \frac{12}{25}

Decimal Notation

5.30831 \dots

Solution steps

\int_{1}^{5} 3 x^{- 1} + x^{- 3} d x

Simplify

3 x^{- 1} + x^{- 3} : \frac{3}{x} + \frac{1}{x ^{3}}

= \int_{1}^{5} \frac{3}{x} + \frac{1}{x ^{3}} 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}^{5} \frac{3}{x} d x + \int_{1}^{5} \frac{1}{x ^{3}} d x

\int_{1}^{5} \frac{3}{x} d x = 3 ln (5)

\int_{1}^{5} \frac{1}{x ^{3}} d x = \frac{12}{25}

= 3 ln (5) + \frac{12}{25}

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What is the integral from 1 to 5 of (3x^{-1}+x^{-3}) ?
The integral from 1 to 5 of (3x^{-1}+x^{-3}) is 3ln(5)+12/25