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

MCQ

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

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

✓

Answer

Correct option: C.

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

c
${\rm{I}} = \int {\frac{{{\rm{dx}}}}{{\rm{x}}}} - \int {\frac{{2{{\rm{x}}^6}}}{{1 + {{\rm{x}}^7}}}} {\rm{dx}}$

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