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∫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.
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