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AP EAMCET20226 Jul 2022Evening ShiftMathematicsIndefinite IntegrationActual

^4 x ( ^2 x+ ⁻³ x ^5 x )^3 d x=

Options

  1. A1 5 (1+ ^5 x )⁻²+C
  2. B1 10 (1+ ^2 x )⁻⁵+C
  3. C1 10 (1+ ^5 x )⁻²+C
  4. D1 5 (1+ ^5 x )⁻⁵+C

Correct answer

C. 1 10 (1+ ^5 x )⁻²+C

Step-by-step solution

aligned & Let I= ^4 x ( ^2 x+ ⁻³ x ^5 x )^3 d x & = ^4 x ( ^2 x )^3 (1+ ^5 x )^3 & = ^4 x cosec ^2 x (1+ ^5 x )^3 d x 1+ ^5 x=y & 5 ^4 x (- cosec ^2 x ) d x=d y & ^4 x cosec ^2 x d x= -1 5 d y & I= -1 5 1 y^3 d y= -1 5 y⁻² -2 & = 1 10 y⁻²+C & = 1 10 [1+ ^5 x ]⁻²+C aligned

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