sinx-x-dx-Mastermind-

Question Number 174770 by Mastermind last updated on 10/Aug/22

\int (\frac{sinx}{\sqrt{x}}) dx

Mastermind

Answered by Frix last updated on 10/Aug/22

\int \frac{\sin x}{\sqrt{x}} d x \overset{(*)}{=} \sqrt{2 π} \int \sin \frac{π u^{2}}{2} d u which is the

Fresnel - Integral = \sqrt{2 π} S (u) . the answer is

\int \frac{\sin x}{\sqrt{x}} d x = \sqrt{2 π} S \sqrt{\frac{2 x}{π}} + C

(*) let u = \sqrt{\frac{2 x}{π}} \Rightarrow d x = \sqrt{2 π x}

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