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# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int\left(x+\frac{2}{x}\right)^2dx$

Learn how to solve calculus problems step by step online.

$\int\left(x^2+\frac{4x}{x}+\frac{4}{x^2}\right)dx$

Learn how to solve calculus problems step by step online. Calculate the integral of int((x+(2/x))^2)dx. A binomial squared (sum) is equal to the square of the first term, plus the double product of the first by the second, plus the square of the second term. In other words: (a+b)^2=a^2+2ab+b^2<ul><li>Square of the first term: \left(x\right)^2 = x^2</li><li>Double product of the first by the second: 2\left(x\right)\left(\frac{2}{x}\right) = 2x\left(\frac{2}{x}\right)</li><li>Square of the second term: \left(\frac{2}{x}\right)^2 = \left(\frac{2}{x}\right)^2</li></ul>. Simplifying. The integral \int x^2dx results in: \frac{x^{3}}{3}. The integral \int4dx results in: 4x.

## Final Answer

$\frac{x^{3}}{3}+4x+\frac{-4}{x}+C_0$

### Problem Analysis

$\int\left(x+\frac{2}{x}\right)^2dx$

Calculus

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