- #1

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## Homework Statement

[Intgrl]ln(x^(2)+4)dx

## Homework Equations

[Intgrl]udv=uv-[Intgrl]vdu

## The Attempt at a Solution

[Intgrl]ln(x^(2)+4)dx, u=ln(x^(2)+4), du=(2x/x^(2)+4), dv=dx, v=x

xln(x^(2)+4)-[Intgrl](2x^(2)/(x^(2)+4))dx

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- Thread starter abel216
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- #1

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[Intgrl]ln(x^(2)+4)dx

[Intgrl]udv=uv-[Intgrl]vdu

[Intgrl]ln(x^(2)+4)dx, u=ln(x^(2)+4), du=(2x/x^(2)+4), dv=dx, v=x

xln(x^(2)+4)-[Intgrl](2x^(2)/(x^(2)+4))dx

- #2

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[tex] \int \frac{2x^2}{x^2 + 4} dx = 2 \int \left( 1 - \frac{1}{1 + \left(\frac{x}{2}\right)^2} \right) dx [/tex]

and substitute [tex] t = \frac{x}{2} [/tex]. (You do know how to integrate [tex] \frac{1}{1 + x^2} [/tex], right?)

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