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Category: Integration

x-4-x-x-1-3-dx-

Question Number 78251 by aliesam last updated on 15/Jan/20 $$\int\frac{{x}+\mathrm{4}}{{x}−\sqrt[{\mathrm{3}}]{{x}}}\:{dx}\: \\ $$ Answered by john santu last updated on 15/Jan/20 $${let}\:{x}\:=\:{u}^{\mathrm{3}} \:\Rightarrow{dx}=\mathrm{3}{u}^{\mathrm{2}} \:{du} \\ $$$$\int\:\frac{{u}^{\mathrm{3}}…

find-cos-2-2x-dx-

Question Number 12702 by mad last updated on 29/Apr/17 $${find}\:\int{cos}^{\mathrm{2}} \mathrm{2}{x}\:{dx} \\ $$ Answered by Joel577 last updated on 29/Apr/17 $$\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}\:=\:\frac{\mathrm{1}\:+\:\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{2}} \\ $$$$\int\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}\:{dx}…

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}}…