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Question Number 137083 by mnjuly1970 last updated on 29/Mar/21

$$\mathit{\varphi }={\int }^{}sin\left(\frac{2}{x}\right)\sqrt{1+{cos}^2\left(\frac{1}{x}\right)}\frac{dx}{x^2}$$

Answered by Ar Brandon last updated on 29/Mar/21

$$\mathrm{\varnothing }=\int \sin \left(\frac{2}{\mathrm{x}}\right)\sqrt{1+{\cos }^2\left(\frac{1}{\mathrm{x}}\right)}\frac{\mathrm{dx}}{{\mathrm{x}}^2}$$$$\mathrm{u}={\cos }^2\left(\frac{1}{\mathrm{x}}\right)\Rightarrow \mathrm{du}=\frac{2}{{\mathrm{x}}^2}\sin \left(\frac{1}{\mathrm{x}}\right)\cos \left(\frac{1}{\mathrm{x}}\right)\mathrm{dx}$$$$\mathrm{\varnothing }=\int \sqrt{1+\mathrm{u}}\mathrm{du}=\frac{2{(1+\mathrm{u})}^{3/2}}{3}+\mathrm{C}$$$$=\frac{2}{3}{[1+{\cos }^2\left(\frac{1}{\mathrm{x}}\right)]}^{3/2}+\mathrm{C}$$

Commented by mohammad17 last updated on 29/Mar/21

$$puttheangleofsinis\left(\frac{2}{x}\right)$$$$$$$$sin\left(\frac{2}{x}\right)\ne sin\left(\frac{1}{x}\right)$$$$$$

Commented by mnjuly1970 last updated on 29/Mar/21

$$thanksalot..$$

Commented by Ar Brandon last updated on 29/Mar/21

$$\sin \left(\frac{2}{\mathrm{x}}\right)=2\sin \left(\frac{1}{\mathrm{x}}\right)\cos \left(\frac{1}{\mathrm{x}}\right)$$

Commented by Ar Brandon last updated on 29/Mar/21

You're welcome, Sir

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