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Step-by-step Solution

Integrate $\sqrt{\frac{3x+8}{x\left(x-2\right)^2}}$ from $5$ to $8$

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Answer

$-\frac{29}{76}y$

Step-by-step explanation

Problem to solve:

$\int_5^8\left(\sqrt{\frac{\left(3x+8\right)}{\left(x\left(x-2\right)^2\right)}}\right)dy$
1

The integral of a constant is equal to the constant times the integral's variable

$\left[\sqrt{\frac{3x+8}{x\left(x-2\right)^2}}y\right]_{5}^{8}$
2

Evaluate the definite integral

$\sqrt{\frac{3\cdot 8+8}{8\left(8-2\right)^2}}y-1\sqrt{\frac{3\cdot 5+8}{5\left(5-2\right)^2}}y$

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Answer

$-\frac{29}{76}y$
$\int_5^8\left(\sqrt{\frac{\left(3x+8\right)}{\left(x\left(x-2\right)^2\right)}}\right)dy$

Main topic:

Definite integrals

Used formulas:

1. See formulas

Time to solve it:

~ 0.74 seconds