Search 73,740 tutors
FIND TUTORS
Ask a question
0 0

(dx)/(x^7-x)

Tutors, please sign in to answer this question.

1 Answer


∫1/(x^7-x) dx
 
1/(x^7-x) ==>> 1/((1-1/x^6) x^7)

= ∫ 1/((1-1/x^6) x^7) dx
 
substitute u = 1-1/x^6  and  du = 6/x^7 dx
 
= 1/6 ∫ 1/u du

The integral of 1/u is ln(u)
 
= (ln(u))/6+constant

Substitute back for u = 1-1/x^6
 
  = 1/6 ln(1-1/x^6)+constant

Which is equivalent for restricted x values to:

  = 1/6 ln(1-x^6)-ln(x)+constant
 

Woodbridge Integrals tutors