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# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve definite integrals problems step by step online.

$\int_{5}^{8}\frac{\sqrt{3x+8}}{\sqrt{x\left(x-2\right)^2}}dy$

Learn how to solve definite integrals problems step by step online. Integrate ((3x+8)/(x(x-2)^2))^0.5 from 5 to 8. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. The integral of a constant is equal to the constant times the integral's variable. Multiplying the fraction by y. Evaluate the definite integral.

## Answer

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

### Problem Analysis

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

### Main topic:

Definite integrals

~ 1.77 seconds