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

The integral from 1 to 3 of (3x^2-7)/(x^3) is 3ln(3)-28/9

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

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

3 ln (3) - \frac{28}{9}

Decimal Notation

0.18472 \dots

Solution steps

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

Expand

\frac{3 x ^{2} - 7}{x ^{3}} : \frac{3}{x} - \frac{7}{x ^{3}}

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

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

\int_{1}^{3} \frac{7}{x ^{3}} d x = \frac{28}{9}

= 3 ln (3) - \frac{28}{9}

\frac{d P}{d t} = k P^{1.01}, P (0) = 10

y^{^{''}} + 2 y^{^{'}} + 5 y = 6 sin (2 t)

\frac{d ^{2}}{d x ^{2}} (cos (5 x))

x \to 0 lim (\frac{a ^{x} - b ^{x}}{x})

y = 2 x^{2}, (- 2, 8)

What is the integral from 1 to 3 of (3x^2-7)/(x^3) ?
The integral from 1 to 3 of (3x^2-7)/(x^3) is 3ln(3)-28/9