∫e^2x*(4x+3)dx
=1/2*∫(4x+3)*e^2xd2x
=1/2∫(4x+3)de^2x
=1/2(4x+3)e^2x-1/2*∫e^2xd(4x+3)
=1/2(4x+3)e^2x-1/2*∫e^2x*4*dx
=1/2(4x+3)e^2x-1/2*2*∫e^2x*2*dx
=1/2(4x+3)e^2x-∫e^2x*d2x
=1/2(4x+3)e^2x-∫de^2x
=1/2(4x+3)e^2x-e^2x+C
∫e^2x*(4x+3)dx
=1/2*∫(4x+3)*e^2xd2x
=1/2∫(4x+3)de^2x
=1/2(4x+3)e^2x-1/2*∫e^2xd(4x+3)
=1/2(4x+3)e^2x-1/2*∫e^2x*4*dx
=1/2(4x+3)e^2x-1/2*2*∫e^2x*2*dx
=1/2(4x+3)e^2x-∫e^2x*d2x
=1/2(4x+3)e^2x-∫de^2x
=1/2(4x+3)e^2x-e^2x+C