Integrating sin(x^2) using substitution method

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SUMMARY

The integral of sin(x^2) cannot be expressed in terms of elementary functions. To compute this integral, the substitution method is employed by letting u = x^2, which leads to du = 2x dx. The integral is then transformed into ∫sin(u) * (1/2x) du. The final result is -(1/2x) * cos(x^2) + C, where C represents the constant of integration.

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how to integrate sin(x^2)?
 
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It can be put in connection with S,which is one of the Fresnel integrals.

It's noit expressible through "elementary" functions.

Daniel.
 

To integrate sin(x^2), we can use the substitution method. Let u = x^2, then du = 2x dx. We can rewrite the integral as ∫sin(u) * (1/2x) du. Using the formula for the integral of sin(u), we get ∫sin(u) * (1/2x) du = -(1/2x) * cos(u) + C = -(1/2x) * cos(x^2) + C. Therefore, the integral of sin(x^2) is -(1/2x) * cos(x^2) + C.
 

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