Step-by-step Solution

Integrate $\left(w+\frac{2}{w}\right)^2$ with respect to w

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Step-by-step explanation

Problem to solve:

$\int\left(w+\frac{2}{w}\right)^2dw$

Learn how to solve calculus problems step by step online.

$\int\left(w^2+\frac{4w}{w}+\frac{4}{w^2}\right)dw$

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Learn how to solve calculus problems step by step online. Calculate the integral of (w+2/w)^2. 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(w\right)^2 = w^2</li><li>Double product of the first by the second: 2\left(w\right)\left(\frac{2}{w}\right) = 2w\left(\frac{2}{w}\right)</li><li>Square of the second term: \left(\frac{2}{w}\right)^2 = \left(\frac{2}{w}\right)^2</li></ul>. Simplifying. The integral \int w^2dw results in: \frac{w^{3}}{3}. The integral \int4dw results in: 4w.

Final Answer

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

Problem Analysis

$\int\left(w+\frac{2}{w}\right)^2dw$

Main topic:

Calculus

Related formulas:

4. See formulas

Time to solve it:

~ 0.08 seconds