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

The integral from 2 to 5 of (4-3x^2)/(x^3) is 21/50-3(ln(5)-ln(2))

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

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

\frac{21}{50} - 3 (ln (5) - ln (2))

Decimal

- 2.32887 \dots

Solution steps

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

Expand

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

= \int_{2}^{5} \frac{4}{x ^{3}} - \frac{3}{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_{2}^{5} \frac{4}{x ^{3}} d x - \int_{2}^{5} \frac{3}{x} d x

\int_{2}^{5} \frac{4}{x ^{3}} d x = \frac{21}{50}

\int_{2}^{5} \frac{3}{x} d x = 3 (ln (5) - ln (2))

= \frac{21}{50} - 3 (ln (5) - ln (2))

\int_{- 1}^{2} - x^{4} - x^{2} + 6 x + 8 d x

\int_{- 1}^{\infty} 3^{- x} d x

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

\int_{4}^{e^{x}} (y^{5} sin (y)) d y

\int_{- 1}^{2} y d y

What is the integral from 2 to 5 of (4-3x^2)/(x^3) ?
The integral from 2 to 5 of (4-3x^2)/(x^3) is 21/50-3(ln(5)-ln(2))