∫x√2x+3 dx的求导过程.

2个回答

∫x√(2x+3)dx
=(1/2)∫(2x+3)√(2x+3)dx-(1/2)∫3√(2x+3)dx
=(1/4)∫√(2x+3)^3d(2x+3) -(3/4)∫√(2x+3)d(2x+3)
=(1/4)(2/5)√(2x+3)^5 -(3/4)*(2/3)√(2x+3)^3+C
=(1/10)√(2x+3)^5 -(1/2)√(2x+3)^3 +C