What is the integral of (sin(x^2))/(x^2) ?

The integral of (sin(x^2))/(x^2) is -(sin(x^2))/x+sqrt(2)sqrt(pi)\C(sqrt(2/pi)x)+C

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integral of (sin(x^2))/(x^2)

\int \frac{sin ( x ^{2} )}{x ^{2}} d x

- \frac{sin ( x ^{2} )}{x} + 2 π C (\frac{2}{π} x) + C

Solution steps

\int \frac{sin ( x ^{2} )}{x ^{2}} d x

Apply Integration By Parts

: - \frac{sin ( x ^{2} )}{x} - \int - 2 cos (x^{2}) d x

= - \frac{sin ( x ^{2} )}{x} - \int - 2 cos (x^{2}) d x

\int - 2 cos (x^{2}) d x = - 2 π C (\frac{2}{π} x)

= - \frac{sin ( x ^{2} )}{x} - (- 2 π C (\frac{2}{π} x))

Simplify

= - \frac{sin ( x ^{2} )}{x} + 2 π C (\frac{2}{π} x)

Add a constant to the solution

= - \frac{sin ( x ^{2} )}{x} + 2 π C (\frac{2}{π} x) + C

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What is the integral of (sin(x^2))/(x^2) ?
The integral of (sin(x^2))/(x^2) is -(sin(x^2))/x+sqrt(2)sqrt(pi)\C(sqrt(2/pi)x)+C