What is the integral from 2 to 5 of (6-x)/(x^3) ?

The integral from 2 to 5 of (6-x)/(x^3) is 33/100

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integral from 2 to 5 of (6-x)/(x^3)

\int_{2}^{5} \frac{6 - x}{x ^{3}} d x

\frac{33}{100}

Decimal Notation

0.33

Solution steps

\int_{2}^{5} \frac{6 - x}{x ^{3}} d x

Expand

\frac{6 - x}{x ^{3}} : \frac{6}{x ^{3}} - \frac{1}{x ^{2}}

= \int_{2}^{5} \frac{6}{x ^{3}} - \frac{1}{x ^{2}} 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_{2}^{5} \frac{6}{x ^{3}} d x - \int_{2}^{5} \frac{1}{x ^{2}} d x

\int_{2}^{5} \frac{6}{x ^{3}} d x = \frac{63}{100}

\int_{2}^{5} \frac{1}{x ^{2}} d x = \frac{3}{10}

= \frac{63}{100} - \frac{3}{10}

Simplify

\frac{63}{100} - \frac{3}{10} : \frac{33}{100}

= \frac{33}{100}

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What is the integral from 2 to 5 of (6-x)/(x^3) ?
The integral from 2 to 5 of (6-x)/(x^3) is 33/100