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Category: Integration

Question-109342

Question Number 109342 by 150505R last updated on 22/Aug/20 Commented by maths mind last updated on 23/Aug/20 x=tg(t),dx=(1+tg2(t))dt$$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\frac{{cos}^{\mathrm{2}} \left({t}\right)−{sin}^{\mathrm{2}} \left({t}\right)}{{sin}\left({t}\right){cos}\left({t}\right)}\right).{dt}…

Question-43731

Question Number 43731 by Meritguide1234 last updated on 14/Sep/18 Answered by MJS last updated on 14/Sep/18 $$\int\left(\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}+\frac{\mathrm{1}}{\mathrm{3}}}{{x}^{\mathrm{3}} −{x}+\mathrm{1}}\right)^{\mathrm{2}} {dx}=\frac{\mathrm{1}}{\mathrm{9}}\int\frac{\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{1}\right)^{\mathrm{2}} }{\left({x}^{\mathrm{3}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \