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

The integral from 1 to 2 of (2x+3/x)^2 is 155/6

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

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

\frac{155}{6}

Decimal Notation

25.83333 \dots

Solution steps

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

Simplify

(2 x + \frac{3}{x})^{2} : 4 x^{2} + 12 + \frac{9}{x ^{2}}

= \int_{1}^{2} 4 x^{2} + 12 + \frac{9}{x ^{2}} 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}^{2} 4 x^{2} d x + \int_{1}^{2} 12 d x + \int_{1}^{2} \frac{9}{x ^{2}} d x

\int_{1}^{2} 4 x^{2} d x = \frac{28}{3}

\int_{1}^{2} 12 d x = 12

\int_{1}^{2} \frac{9}{x ^{2}} d x = \frac{9}{2}

= \frac{28}{3} + 12 + \frac{9}{2}

Simplify

\frac{28}{3} + 12 + \frac{9}{2} : \frac{155}{6}

= \frac{155}{6}

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What is the integral from 1 to 2 of (2x+3/x)^2 ?
The integral from 1 to 2 of (2x+3/x)^2 is 155/6