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Integral of (x-x^5)^(1÷5) /x^6 dx,how to find this,I need a complete solution

Integral of (x-x^5)^(1÷5) /x^6 dx,how to find this,I need a complete solution

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
Int of (x-x^5)^1/5/x^6 dx
              = Int of [(x^5)^1/5 .  (1/x^4 – 1)^1/5]/x^6 dx
              = Int of (1/x^4-1)^1÷5 / x^5 dx
              Suppose, 1/x^4 – 1= z
             So,dz = -4/x^5 dx
               So, 1/x^5 dx = - ¼ dz
            Putting the values we get,
-1/4  Int of z^1/5 dz
            = -1/4 x. 5/6 . z^6/5 + c
           = - 5/24 ( 1/x^4-1)^6/5  + c  ( putting the values) .
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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