Verified Solution • 2025–26 Session moderate

QJEEM21Mabf03: JEE Main 2021 Mathematics - Class 12 JEEM21Mabf03 Solution: The integral ∫ 1 ( x − 1 ) 3 ( x + 2 ) 5 4 d x is equal to :…

The integral ∫1(x−1)3(x+2)54dx is equal to : (where C is a constant of integration)

Multiple Choice Options

  • A 34(x+2x−1)14+C{3 \over 4}{\left( {{{x + 2} \over {x - 1}}} \right)^{{1 \over 4}}} + C
  • B 34(x+2x−1)54+C{3 \over 4}{\left( {{{x + 2} \over {x - 1}}} \right)^{{5 \over 4}}} + C
  • C 43(x−1x+2)14+C{4 \over 3}{\left( {{{x - 1} \over {x + 2}}} \right)^{{1 \over 4}}} + C
  • D 43(x−1x+2)54+C{4 \over 3}{\left( {{{x - 1} \over {x + 2}}} \right)^{{5 \over 4}}} + C

Step-by-Step Verified Solution

∫dx(x−1)3/4(x+2)5/4\int {{{dx} \over {{{(x - 1)}^{3/4}}{{(x + 2)}^{5/4}}}}}

=∫dx(x+2x−1)5/4. (x−1)2= \int {{{dx} \over {{{\left( {{{x + 2} \over {x - 1}}} \right)}^{5/4}}.\,{{(x - 1)}^2}}}}

put x+2x−1=t{{x + 2} \over {x - 1}} = t

=−13∫dtt5/4= - {1 \over 3}\int {{{dt} \over {{t^{5/4}}}}}

=43.1t1/4+C= {4 \over 3}.{1 \over {{t^{1/4}}}} + C

=43(x−1x+2)1/4+C= {4 \over 3}{\left( {{{x - 1} \over {x + 2}}} \right)^{1/4}} + C

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