Question

ln(x)/x^(1/5) вычислить неопределенный интеграл

Answer 1

∫(ln(x)/x^(1/5))dx=∫(ln(x)*x^(-1/5))dx.
∫UdV=U*V-∫VdU
U=ln(x)   dV=x^(-1/5)dx    V=∫(x^(-1/5))dx=(5/4)*(x^(4/5)   dU=(ln(x))`=1/x   ⇒
∫UdV=ln(x)*(5/4)*(x^(4/5)-∫(((5/4)*x^(4/5))/x)dx=
=ln(x)*(5/4)*x^(4/5)-(5/4)*∫x^(-1/5)dx=ln(x)*(5/4)*x^(4/5)-(5/4)*(5/4)*x^(4/5)=
=(5/4)*x^(4/5)*((ln(x)-(5/4)).