Question 564858: Use the method of integration by parts to determine the primitives for this function:
x^1/2 ln x
Help me Answer by ad_alta(240) (Show Source):
You can put this solution on YOUR website! Int(u dv)=uv-Int(v du) {this is integration by parts: I won't prove it, but it isn't difficult to show}. Let u=ln(x) and dv=x^(1/2)dx. Then du=dx/x and v=(2/3)x^(3/2). Thus Int(x^(1/2)ln(x)dx)=(ln(x))*(2/3)x^(3/2)-Int((2/3)x^(3/2)(1/x)dx)=(ln(x))*(2/3)x^(3/2)-Int((2/3)x^(1/2)dx)=(ln(x))*(2/3)x^(3/2)-(4/9)x^(3/2)=MESS
