The next step is to use integration by parts on the second term of the integrand, yielding ∫ ∫ a b [ ∂ ∂ L ∂ ∂ f ( x , f ( x ) , f ′ ( x ) ) − − d d x ∂ ∂ L ∂ ∂ f ′ ( x , f ( x ) , f ′ ( x ) ) ] η η ( x ) d x + [ η η ( x ) ∂ ∂ L ∂ ∂ f ′ ( x , f ( x ) , f ′ ( x ) ) ] a b = 0 .