Question

求解∫cos^2(1-2x)dx,∫(sin ax cos ax) 用第二积分换元法

Answer 1

∫cos^2(1-2x)dx

= ∫ [cos(2-4x)+1]/2 dx

= [ ∫cos(2-4x)dx ]/2+∫(1/2)dx

= -[∫cosudu]/8 +x/2+C

=(-sinu)/8 + x/2+C

=[-sin(2-4x)]/8 +x/2+C

∫(sin ax cos ax) dx

=[ ∫(sin ax)d sinax ]/a

=(sin^2 ax) /2a +C