Помогите решить интегрирование по частям int sqrtx lnx dx

∫ √x ln x dx = √x = t → x = t² → dx = 2t dt ∫ √x ln x dx = ∫ t ln (t²) (2t dt) = ∫ 2t² ln (t²) dt = (t²) = u and 2t²dt = dv; (2t / t²) dt = (2 / t) dt = du  2(t²⁺¹)/(2+1) = (2/3)t³ = v ∫ 2t² ln (t²) dt = (2/3)t³ ln (t²) - ∫ (2/3)t³ (2/ t) dt = (2/3)t³ ln (t²) - (4/3) ∫ (t³/ t) dt = (2/3)t³ ln (t²) - (4/3) ∫ t² dt = (2/3)t³ ln (t²) - (4/3)(t²⁺¹)/(2+1) + c = (2/3)t³ ln (t²) - (4/3)(1/3)t³+ c = (2/3)t³ ln (t²) - (4/9)t³+ c   t = √x ∫ √x ln x dx = (2/3)√x³ ln (√x²) - (4/9)√x³+ c =  (2/3)x√x ln x - (4/9)x√x + c

[latex]\int{\sqrt{x}lnx}\, dx[/latex] [latex]U=lnx[/latex] [latex]dU=\frac{1}{x}dx[/latex] [latex]V=\frac{2}{3}*\sqrt{x^3}[/latex] [latex]\int{\sqrt{x}lnx}\, dx=\frac{2}{3}*\sqrt{x^3}lnx-\int{\frac{2}{3}\sqrt{x^3}}\, dx=\frac{2}{3}*\sqrt{x^3}lnx-\int{\frac{2}{3}\sqrt{x^3}\frac{1}{x}}\, dx=\frac{2}{3}*\sqrt{x^3}lnx-\frac{4}{9}\sqrt{x^3}+C[/latex]