What is the integral from 1 to 2 of 5/(x^6) ?

The integral from 1 to 2 of 5/(x^6) is 31/32

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integral from 1 to 2 of 5/(x^6)

\int_{1}^{2} \frac{5}{x ^{6}} d x

\frac{31}{32}

Solution steps

\int_{1}^{2} \frac{5}{x ^{6}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{1}^{2} \frac{1}{x ^{6}} d x

Apply the Power Rule

: [- \frac{1}{5 x ^{5}}]_{1}^{2}

= 5 [- \frac{1}{5 x ^{5}}]_{1}^{2}

Compute the boundaries:

\frac{31}{160}

= 5 \cdot \frac{31}{160}

Simplify

= \frac{31}{32}

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What is the integral from 1 to 2 of 5/(x^6) ?
The integral from 1 to 2 of 5/(x^6) is 31/32