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Question Number 91904 by Ar Brandon last updated on 03/May/20

$${\int }_1^{{\mathrm{e}}^{\pi }}\frac{\cos \left(\mathrm{lnx}\right)}{\mathrm{x}}\mathrm{dx}$$

Commented by Prithwish Sen 1 last updated on 03/May/20

$$\mathrm{put}\ln \left(\mathrm{x}\right)=\mathrm{t}$$

Commented by Ar Brandon last updated on 03/May/20

$$\mathrm{Okay},\mathrm{let}\mathrm{me}\mathrm{try}.\mathrm{Thanks}$$

Commented by mathmax by abdo last updated on 03/May/20

$$I={\int }_1^{e^{\pi }}\frac{cos\left(lnx\right)}{x}dxvhangementlnx=tgive$$$$I={\int }_0^{\pi }\frac{cos\left(t\right)}{e^t}{e}^{t}dt={\int }_0^{\pi }costdt={\left[sint\right]}_0^{\pi }=0$$

Answered by Ar Brandon last updated on 03/May/20

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