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

The integral from 1 to 3 of (2x^2+3x-2)/x is -2ln(3)+14

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

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

- 2 ln (3) + 14

Decimal Notation

11.80277 \dots

Solution steps

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

Expand

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

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

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 3 d x = 6

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

= 8 + 6 - 2 ln (3)

Simplify

= - 2 ln (3) + 14

\frac{\partial}{\partial s} (\frac{s}{t})

\int \frac{x}{3 x ^{2} - 4} d x

\int - 19 x^{2} - 2 x + 8 d x

\frac{\partial}{\partial x} (1 + x^{3} + y^{3})

g (x) = - \frac{9}{( 6 x + 8 ) ^{\frac{3}{2}}}

What is the integral from 1 to 3 of (2x^2+3x-2)/x ?
The integral from 1 to 3 of (2x^2+3x-2)/x is -2ln(3)+14