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sinx-x-dx-Mastermind-




Question Number 174770 by Mastermind last updated on 10/Aug/22
∫(((sinx)/( (√x))))dx    Mastermind
(sinxx)dxMastermind
Answered by Frix last updated on 10/Aug/22
∫((sin x)/( (√x)))dx=^((∗)) (√(2π))∫sin ((πu^2 )/2) du which is the  Fresnel−Integral =(√(2π))S (u). the answer is  ∫((sin x)/( (√x)))dx=(√(2π))S (√((2x)/π)) +C    (∗) let u=(√((2x)/π)) ⇒ dx=(√(2πx))
sinxxdx=()2πsinπu22duwhichistheFresnelIntegral=2πS(u).theanswerissinxxdx=2πS2xπ+C()letu=2xπdx=2πx

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