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Category: Integration

If-tan-x-1-tan-x-tan-2-x-dx-x-k-A-tan-1-k-tan-x-1-A-C-where-C-is-constant-of-integration-then-the-ordered-pair-k-A-is-equal-to-

Question Number 133004 by liberty last updated on 18/Feb/21 $$\mathrm{If}\:\int\:\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{1}+\mathrm{tan}\:\mathrm{x}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}\:=\:\mathrm{x}−\frac{{k}}{\:\sqrt{{A}}}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{{k}\:\mathrm{tan}\:{x}+\mathrm{1}}{\:\sqrt{{A}}}\right)+\mathrm{C} \\ $$$$\mathrm{where}\:\mathrm{C}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{integration}. \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{ordered}\:\mathrm{pair}\:\left({k},\mathrm{A}\right)\:\mathrm{is}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\: \\ $$ Answered by EDWIN88 last updated…

mathematical-analysis-prove-that-0-sin-3-x-x-3-dx-3pi-8-

Question Number 132987 by mnjuly1970 last updated on 17/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{mathematical}\:\:{analysis}… \\ $$$$\:{prove}\:\:{that}::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{3}} }{dx}=\frac{\mathrm{3}\pi}{\mathrm{8}} \\ $$$$\:\:\:\:\ast\ast\ast\ast………. \\ $$$$ \\ $$ Answered by Dwaipayan…