Question

cosy^2/y integration dy.​

Answer 1

Let

$I = \int \frac{ { \cos}^{2} (y)}{y} dy = \frac{Ci(2y) + ln(y) }{2} + C$

where, C ∈ ℝ

Where, Ci(z) is the cosine integral function.

As, This function has non elementary antiderivative, so we need special functions to define it.

If,

$I = \int \frac{ \cos( {y}^{2} ) }{y} dy$

Then,

$I = \frac{Ci( {y}^{2} )}{2} + C$