Find the anti derivative of cos √x . Please include the description too

∫cos(√x)=?

Let u = √x 
=> du = (1 / 2√x) dx 
=> 2 du = (1 / √x) dx 
=> 2 du = (1/u) dx

=> 2u du = dx

Replace the value of √x and dx

=> ∫ 2u cos(u) du

Integration by parts (Using ILATE method)

Let w = 2u 
=> dw = 2 du 
Let dv = cos(u) du 
=> v = sin(u)

=> 2u sin(u) - 2 ∫ sin(u) du

=> sin(u) + 2cos(u)

∫cos(√x)= 2√x sin(√x) + 2cos(√x) Ans.