What is the integral from 1 to 3 of (15+2x^3)/(x^4) ?

The integral from 1 to 3 of (15+2x^3)/(x^4) is 130/27+2ln(3)

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integral from 1 to 3 of (15+2x^3)/(x^4)

\int_{1}^{3} \frac{15 + 2 x ^{3}}{x ^{4}} d x

\frac{130}{27} + 2 ln (3)

Decimal

7.01203 \dots

Solution steps

\int_{1}^{3} \frac{15 + 2 x ^{3}}{x ^{4}} d x

Expand

\frac{15 + 2 x ^{3}}{x ^{4}} : \frac{15}{x ^{4}} + \frac{2}{x}

= \int_{1}^{3} \frac{15}{x ^{4}} + \frac{2}{x} 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}^{3} \frac{15}{x ^{4}} d x + \int_{1}^{3} \frac{2}{x} d x

\int_{1}^{3} \frac{15}{x ^{4}} d x = \frac{130}{27}

\int_{1}^{3} \frac{2}{x} d x = 2 ln (3)

= \frac{130}{27} + 2 ln (3)

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What is the integral from 1 to 3 of (15+2x^3)/(x^4) ?
The integral from 1 to 3 of (15+2x^3)/(x^4) is 130/27+2ln(3)