What is the integral from 1 to 2 of (x^5+x^{-5}) ?

The integral from 1 to 2 of (x^5+x^{-5}) is 687/64

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integral from 1 to 2 of (x^5+x^{-5})

\int_{1}^{2} (x^{5} + x^{- 5}) d x

\frac{687}{64}

Decimal Notation

10.734375

Solution steps

\int_{1}^{2} x^{5} + x^{- 5} 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}^{2} x^{5} d x + \int_{1}^{2} x^{- 5} d x

\int_{1}^{2} x^{5} d x = \frac{21}{2}

\int_{1}^{2} x^{- 5} d x = \frac{15}{64}

= \frac{21}{2} + \frac{15}{64}

Simplify

\frac{21}{2} + \frac{15}{64} : \frac{687}{64}

= \frac{687}{64}

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What is the integral from 1 to 2 of (x^5+x^{-5}) ?
The integral from 1 to 2 of (x^5+x^{-5}) is 687/64