Here y is constant ,Since integration is with respect to x .
⟹I=∫sin(xy)2.
Let xy=u⟹dx=y1du.
⟹I=y1∫sinu2du.
By fundamental theorem of calculus ,every continuous real function f has an anti derivative but some ordinary looking continuous function have anti derivative that can not expressed in simple formula using more basic function. I looks like one of them.
I is called Fresnel integral which is a transcendental function.
I admits the following power series expansion that converges for all x .
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