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Joint Entrance Examination
Mathematics
Indefinite Integrals
Question 382
Question 382 of 416
Medium
MCQ
The integral \[\int {{{2{x^3} - 1} \over {{x^4} + x}}} dx\] is equal to : (Here C is a constant of integration)
A
\[{\log _e}{{\left| {{x^3} + 1} \right|} \over {{x^2}}} + C\]
B
\[{1 \over 2}{\log _e}{{\left| {{x^3} + 1} \right|} \over {{x^2}}} + C\]
C
\[{\log _e}\left| {{{{x^3} + 1} \over x}} \right| + C\]
D
\[{1 \over 2}{\log _e}{{{{\left( {{x^3} + 1} \right)}^2}} \over {\left| {{x^3}} \right|}} + C\]
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Official solution
\[\int {{{2{x^3} - 1} \over {{x^4} + x}}dx = \int {{{2x - {x^{ - 2}}} \over {{x^2} + {x^{ - 1}}}}dx = \ln ({x^2} + {x^{ - 1}}} } ) + c\] \[ \Rightarrow \ln ({x^3} + 1) - \ln x + c\]
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