What is the integral from 1 to 2 of (x^3)/2+1/(2x^3) ?

The integral from 1 to 2 of (x^3)/2+1/(2x^3) is 33/16

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integral from 1 to 2 of (x^3)/2+1/(2x^3)

\int_{1}^{2} \frac{x ^{3}}{2} + \frac{1}{2 x ^{3}} d x

\frac{33}{16}

Decimal Notation

2.0625

Solution steps

\int_{1}^{2} \frac{x ^{3}}{2} + \frac{1}{2 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}^{2} \frac{x ^{3}}{2} d x + \int_{1}^{2} \frac{1}{2 x ^{3}} d x

\int_{1}^{2} \frac{x ^{3}}{2} d x = \frac{15}{8}

\int_{1}^{2} \frac{1}{2 x ^{3}} d x = \frac{3}{16}

= \frac{15}{8} + \frac{3}{16}

Simplify

\frac{15}{8} + \frac{3}{16} : \frac{33}{16}

= \frac{33}{16}

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What is the integral from 1 to 2 of (x^3)/2+1/(2x^3) ?
The integral from 1 to 2 of (x^3)/2+1/(2x^3) is 33/16