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I am doing a problem with PDF's and this integral is a roadblock.

I have $f(x)=\dfrac{200}{(x+10)^3}$ where $x>0$ and have solved that $\mathbb{E}(X)=10$.

I am working on finding $\mathbb{E}(X^2)$ and so far have $\mathbb{E}(X^2)=\displaystyle \int_0^\infty \frac{200x^2}{(x+10)^3}$.

How do I go about showing that $\mathbb{E}(X^2)$ diverges? I tried substitution but it doesn't seem to work

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Note that $\frac{x^2}{(x+10)^3}\sim \frac{1}{x}$ – Pedro Tamaroff Mar 19 '12 at 22:20

Comparison to $\int_1^{\infty}x^{-1}\,dx$.

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Using partial fractions $$\int \frac{200 x^2}{(x+10)^3} dx = \frac{4000}{x+10} - \frac{10000}{(x+10)^2} +200 \, \log_e(x+10)+c$$

and $\log_e(x+10)$ increases without limit as $x$ increases.

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