What is the antiderivative of #(5 ln(x))/x^(7) #?
1 Answer
Jul 31, 2016
Explanation:
We have:
#5intln(x)/x^7dx#
We will want to use integration by parts, which takes the form:
#intudv=uv-intvdu#
So here, let
Thus:
#5intln(x)/x^7dx=5[-1/6ln(x)x^-6-int-1/6x^-6(1/x)dx]#
#=-5/6ln(x)/x^6+5/6intx^-7dx#
#=-(5ln(x))/(6x^6)+5/6(-1/6x^-6)+C#
#=-(5ln(x))/(6x^6)-5/(36x^6)+C#
If you want a common denominator:
#=-(30ln(x)+5)/(36x^6)+C#