The integral ∫log $$5log$$ $$7$$ xcos $$x2cos$$ log $$35$$−$$x2+$$$$cos$$ $$x2dx$$ is equal to

Question

The integral ∫log $$5log$$ $$7$$ xcos $$x2cos$$ log $$35$$−$$x2+$$$$cos$$ $$x2dx$$ is equal to

Infinity Learn · Accepted Answer

∫log $$5log$$ $$7$$ xcos $$x2cos$$ log $$35$$−$$x2+$$$$cos$$ $$x2dx=12$$∫log $$5log$$ $$7$$ $$cos$$ tcos (log$$ $$35$$−$$t)+$$$$cos$$ $$tdtx2=t=12I$$′I′$$=$$∫log $$5log$$ $$7$$ $$cos$$$$(log$$ $$7+log$$ $$5$$−$$t)$$cos$$ $$t+$$$$cos$$(log7+log$$ $$5$$−$$t)dt=$$∫log $$5log7$$ $$cos$$ $$(log$$ $$35$$−$$t)cost+$$$$cos$$ $$(log$$ $$35$$−$$t)dt2I$$′$$=I$$′$$+I$$′$$=$$∫log $$5log7$$ $$cos$$ $$t+$$$$cos$$$$(log$$ $$35$$−$$t)$$cos$$ $$t+$$$$cos$$$$(log$$ $$35$$−$$t)dt=log$$ $$75$$⇒$$I=14log$$ $$75$$

The integral $\int_{\sqrt{\log 5}}^{\sqrt{\log 7}} \frac{x \cos x^{2}}{\cos (\log 35 - x^{2}) + \cos x^{2}} d x$ is
equal to

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The integral ∫log 5log 7 xcos x2cos log 35−x2+cos x2dx is equal to

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The integral $\int_{\sqrt{\log 5}}^{\sqrt{\log 7}} \frac{x \cos x^{2}}{\cos (\log 35 - x^{2}) + \cos x^{2}} d x$ is
equal to