, , 1 - x^7 x(1 + x^7 ) dx equals : - Vidyadip

MCQ

$\int {\,\,\frac{{1 - {x^7}}}{{x(1 + {x^7})}}} $ $dx $ equals :

A
$ln x + \frac{2}{7} ln (1 + x^7) + c$
B
$ln x - \frac{2}{7} ln (1 - x^7) + c$
✓
$ln x - \frac{2}{7} ln (1 + x^7) + c$
D
$ln x + \frac{2}{7} ln (1 - x^7) + c$

✓

Answer

Correct option: C.

$ln x - \frac{2}{7} ln (1 + x^7) + c$

c
$I =$ $\int {\,\,\frac{{dx}}{{x\,\,\left( {1\,\, + \,\,{x^7}} \right)}}} $ -$\int {\,\,\frac{{{x^6}}}{{1\,\, + \,\,{x^7}}}} dx $

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