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Category: Integration

Study-the-convergence-with-respect-to-and-the-improper-integral-below-0-dx-x-lnx-

Question Number 143755 by Ar Brandon last updated on 18/Jun/21 $$\mathrm{Study}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to} \\ $$$$\alpha\:\mathrm{and}\:\beta\:\mathrm{the}\:\mathrm{improper}\:\mathrm{integral}\:\mathrm{below}; \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\mathrm{x}^{\alpha} \left(\mathrm{lnx}\right)^{\beta} } \\ $$ Answered by mathmax by…

Question-12635

Question Number 12635 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 27/Apr/17 Answered by mrW1 last updated on 27/Apr/17 $${x}^{\mathrm{2}} −\mathrm{2}{x}\mathrm{tan}\:\varphi−\mathrm{1} \\ $$$$={x}^{\mathrm{2}} −\mathrm{2}{x}\mathrm{tan}\:\varphi+\mathrm{tan}^{\mathrm{2}} \:\varphi−\mathrm{1}−\mathrm{tan}^{\mathrm{2}} \:\varphi \\ $$$$=\left({x}−\mathrm{tan}\:\varphi\right)^{\mathrm{2}}…

1-3-sin-sin-2-d-

Question Number 78163 by TawaTawa last updated on 14/Jan/20 $$\int\:\sqrt{\mathrm{1}\:+\:\mathrm{3}\:\mathrm{sin}\left(\theta\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\theta\right)}\:\:\mathrm{d}\theta \\ $$ Commented by MJS last updated on 15/Jan/20 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this} \\ $$ Commented by…