What is the integral from 1 to 7 of (4x^2-5)/(x^3) ?

The integral from 1 to 7 of (4x^2-5)/(x^3) is 4ln(7)-120/49

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integral from 1 to 7 of (4x^2-5)/(x^3)

\int_{1}^{7} \frac{4 x ^{2} - 5}{x ^{3}} d x

4 ln (7) - \frac{120}{49}

Decimal

5.33466 \dots

Solution steps

\int_{1}^{7} \frac{4 x ^{2} - 5}{x ^{3}} d x

Expand

\frac{4 x ^{2} - 5}{x ^{3}} : \frac{4}{x} - \frac{5}{x ^{3}}

= \int_{1}^{7} \frac{4}{x} - \frac{5}{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}^{7} \frac{4}{x} d x - \int_{1}^{7} \frac{5}{x ^{3}} d x

\int_{1}^{7} \frac{4}{x} d x = 4 ln (7)

\int_{1}^{7} \frac{5}{x ^{3}} d x = \frac{120}{49}

= 4 ln (7) - \frac{120}{49}

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What is the integral from 1 to 7 of (4x^2-5)/(x^3) ?
The integral from 1 to 7 of (4x^2-5)/(x^3) is 4ln(7)-120/49