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

The integral from 2 to 4 of (2/x+3x)^2 is 193

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

\int_{2}^{4} (\frac{2}{x} + 3 x)^{2} d x

193

Solution steps

\int_{2}^{4} (\frac{2}{x} + 3 x)^{2} d x

Simplify

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

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

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

\int_{2}^{4} 12 d x = 24

\int_{2}^{4} 9 x^{2} d x = 168

= 1 + 24 + 168

Simplify

= 193

\int e^{x} - e^{2 x} d x

\frac{1}{s - 2}

sin (3 x^{5} + 5 x^{4})

x \frac{d y}{d x} + \frac{y}{x + 1} = x (x + 1)

x \to - 1 lim (\frac{x ^{100}}{1})

What is the integral from 2 to 4 of (2/x+3x)^2 ?
The integral from 2 to 4 of (2/x+3x)^2 is 193