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Question Number 77675 by TawaTawa last updated on 08/Jan/20

$${\int }_0^{\mathrm{\infty }}3{(2\mathrm{x}-\frac{3}{\mathrm{x}})}^2\mathrm{dx}$$

Answered by mind is power last updated on 09/Jan/20

$$\mathrm{diverge}$$$$\mathrm{use}\mathrm{that}{\left[(2\mathrm{x}-\frac{3}{\mathrm{x}})\right]}^2⩾1,\mathrm{\forall }\mathrm{x}⩾4$$$$\Rightarrow {\int }_0^{+\mathrm{\infty }}3{(2\mathrm{x}-\frac{3}{\mathrm{x}})}^2\mathrm{dx}⩾{\int }_4^{+\mathrm{\infty }}3.4\mathrm{dx}={\int }_3^{+\mathrm{\infty }}12\mathrm{dx}=+\mathrm{\infty }$$

Commented by TawaTawa last updated on 09/Jan/20

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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