We use integration by substitution. If u = f ′ ( x ) {\displaystyle u=f'(x)} then d u = f ″ ( x ) d x {\displaystyle du=f''(x)dx} . Thus, f ′ ( x ) f ″ ( x ) d x = u d u {\displaystyle f'(x)f''(x)dx=udu} . We also can transform the bounds so that 1 ↦ f ′ ( 1 ) = 2 {\displaystyle 1\mapsto f'(1)=2} and 2 ↦ f ′ ( 2 ) = 3 {\displaystyle 2\mapsto f'(2)=3} . In terms of u, we can integrate: