Use integration by parts to find x^2 ln 5x dx?

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Answer 1 · 2018-03-08T06:44:09

The answer is #=1/3x^3ln(5x)-x^3/9+C#

#intuv'=uv-intu'v#

Here,

#u=ln(5x)#, #=>#, #u'=1/(5x)*5=1/x#

#v'=x^2#, #=>#, #v=1/3x^3#

Therefore,

#intx^2ln(5x)dx=1/3x^3ln(5x)-int1/x*1/3*x^3dx#

#=1/3x^3ln(5x)-x^3/9+C#