Let x^{2} = t, Limit value x = [ 1 , 4 ] => t = [ 1 , 16 ]
And 2x dx = dt
=> 2dx / x = dt / x^{2} = dt / t.
∫ (2 e^{sinx^2} / x) dx
= ∫ (e^{sin t }) / t dt
= ∫ F ' ( t) dt // d/dx [f(x)] = e^{sinx }/ x , x > 0
= [F(t) ]_{1}^{16}
^{= }F(16 ) - F(1)
Ans - k= 16.