Evaluating int 1/(x^7-x)dx

ajanlr

ajanlr

Answered question

2022-10-30

Evaluating 1 x 7 x   d x

Answer & Explanation

spornya1

spornya1

Beginner2022-10-31Added 18 answers

Answer:
1 x 7 x d x = 1 x 7 . ( 1 1 x 6 ) d x
Put ( 1 1 x 6 ) = t and 6 x 7 d x = d t
= 1 6 1 t d t = 1 6 ln t + C
= 1 6 ln | x 6 1 x 6 | + C
Tessa Peters

Tessa Peters

Beginner2022-11-01Added 4 answers

1 x 7 x d x = 1 x ( x 6 1 ) d x = ( x 5 x 6 1 1 x ) d x = x 5 d x x 6 1 ln | x | = 1 6 ln | x 6 1 | ln | x | + C = 1 6 ln | 1 1 x 6 | + C .
Replacing 6 by n and changing the sign yields the general integral
1 x ( x n ± 1 ) d x = 1 n ln | 1 ± 1 x n | + C

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