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




Question Number 84106 by jagoll last updated on 09/Mar/20
∫ (x^4 /( (√(1−x^4 )))) dx = ?
$$\int\:\frac{\mathrm{x}^{\mathrm{4}} }{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=\:? \\ $$
Commented by MJS last updated on 09/Mar/20
t=(√(sin x)) → dx=((√(1−x^4 ))/(2x))dt  (1/2)∫(sin t)^(3/2) dt  this can be solved using Γ(x)  Sir Tanmay knows how
$${t}=\sqrt{\mathrm{sin}\:{x}}\:\rightarrow\:{dx}=\frac{\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}{\mathrm{2}{x}}{dt} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\int\left(\mathrm{sin}\:{t}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} {dt} \\ $$$$\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{using}\:\Gamma\left({x}\right) \\ $$$$\mathrm{Sir}\:\mathrm{Tanmay}\:\mathrm{knows}\:\mathrm{how} \\ $$

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