∫xlog(x)dx=?
x24[2log(x)–1]+c
x22[2log(x)–1]+c
x24[2log(x)+1]+c
x22[2log(x)+1]+c
Explanation For Correct The Option:
Evaluating the integral:
Given ∫xlog(x)dx
Applying integration by parts,
∫f(x).g(x).dx=f(x).∫g(x).dx-∫(f'(x).∫g(x).dx).dx
∫xlogxdx=logx∫xdx-∫d(logx)dx∫x.dxdx=logxx22-∫1x.x22dx=x22logx-12∫xdx=x22logx-12x22+c=x22logx-x24+c=x242logx-1+c
Hence, the correct answer is option (A).