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\int_{-1}^{2}\left(\left(2+x\right)^2-\left(x^2\right)^2\right)dx\cdot\frac{1}{2}

Integrate (2+x)^2-1x^2^2 from -1 to 2

Answer

$\frac{1}{2}\left(\int_{-1}^{2}-x^{4}dx+21\right)$

Step-by-step explanation

Problem

$\int_{-1}^{2}\left(\left(2+x\right)^2-\left(x^2\right)^2\right)dx\cdot\frac{1}{2}$
1

Applying the power of a power property

$\frac{1}{2}\int_{-1}^{2}\left(\left(x+2\right)^2-x^{4}\right)dx$

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Answer

$\frac{1}{2}\left(\int_{-1}^{2}-x^{4}dx+21\right)$

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$\int_{-1}^{2}\left(\left(2+x\right)^2-\left(x^2\right)^2\right)dx\cdot\frac{1}{2}$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 1.18 seconds