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STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
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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