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2sin-1-x-x-1-x-2-2-x-4-dx-




Question Number 215974 by ajfour last updated on 23/Jan/25
∫(√((2sin^(−1) x−x(√(1−x^2 )))^2 +x^4 ))dx
$$\int\sqrt{\left(\mathrm{2sin}^{−\mathrm{1}} {x}−{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)^{\mathrm{2}} +{x}^{\mathrm{4}} }{dx} \\ $$
Answered by MathematicalUser2357 last updated on 26/Jan/25
No closed forms. ((x∣x∣)/2)+((x^3 ∣x∣)/3)−((2x^5 ∣x∣)/(45))+…
$$\mathrm{No}\:\mathrm{closed}\:\mathrm{forms}.\:\frac{{x}\mid{x}\mid}{\mathrm{2}}+\frac{{x}^{\mathrm{3}} \mid{x}\mid}{\mathrm{3}}−\frac{\mathrm{2}{x}^{\mathrm{5}} \mid{x}\mid}{\mathrm{45}}+\ldots \\ $$

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