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0-1-tan-1-2x-1-1-x-x-2-dx-




Question Number 103683 by Dwaipayan Shikari last updated on 16/Jul/20
∫_0 ^1 tan^(−1) (((2x−1)/(1+x−x^2 )))dx
$$\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{x}−{x}^{\mathrm{2}} }\right){dx} \\ $$
Commented by Dwaipayan Shikari last updated on 16/Jul/20
∫_0 ^1 tan^(−1) (((x+x−1)/(1−x(x−1))))  ∫_0 ^1 tan^(−1) x+tan^(−1) (x−1)  ∫_0 ^1 tan^(−1) (1−x)−tan^(−1) (1−x)=0  Is it???????
$$\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} \left(\frac{{x}+{x}−\mathrm{1}}{\mathrm{1}−{x}\left({x}−\mathrm{1}\right)}\right) \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} {x}+{tan}^{−\mathrm{1}} \left({x}−\mathrm{1}\right) \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)−{tan}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)=\mathrm{0} \\ $$$${Is}\:{it}??????? \\ $$
Answered by maths mind last updated on 16/Jul/20
=∫tg^− (((x+(x−1))/(1−x(x−1))))dx...
$$=\int{tg}^{−} \left(\frac{{x}+\left({x}−\mathrm{1}\right)}{\mathrm{1}−{x}\left({x}−\mathrm{1}\right)}\right){dx}… \\ $$$$ \\ $$

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