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

The integral from 1 to 5 of (x^3+1/(x^3)) is 3912/25

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integral from 1 to 5 of (x^3+1/(x^3))

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

\frac{3912}{25}

Decimal Notation

156.48

Solution steps

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

\int_{1}^{5} x^{3} d x = 156

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

= 156 + \frac{12}{25}

Simplify

156 + \frac{12}{25} : \frac{3912}{25}

= \frac{3912}{25}

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What is the integral from 1 to 5 of (x^3+1/(x^3)) ?
The integral from 1 to 5 of (x^3+1/(x^3)) is 3912/25