What is the integral from 1 to 2 of x^5+1/(4x^5) ?

The integral from 1 to 2 of x^5+1/(4x^5) is 2703/256

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integral from 1 to 2 of x^5+1/(4x^5)

\int_{1}^{2} x^{5} + \frac{1}{4 x ^{5}} d x

\frac{2703}{256}

Decimal

10.55859 \dots

Solution steps

\int_{1}^{2} x^{5} + \frac{1}{4 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} \frac{1}{4 x ^{5}} d x

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

\int_{1}^{2} \frac{1}{4 x ^{5}} d x = \frac{15}{256}

= \frac{21}{2} + \frac{15}{256}

Simplify

\frac{21}{2} + \frac{15}{256} : \frac{2703}{256}

= \frac{2703}{256}

What is the integral from 1 to 2 of x^5+1/(4x^5) ?
The integral from 1 to 2 of x^5+1/(4x^5) is 2703/256