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KCET2021MathematicsIndefinite Integration

The value of x² d x x⁶+a⁶ is equal to

Options

  1. A|x³+ x⁶+a⁶ |+C
  2. B|x³- x⁶+a⁶ |+C
  3. C1 3 |x³+ x⁶+a⁶ |+C
  4. D1 3 |x³- x⁶+a⁶ |+C

Correct answer

C. 1 3 |x³+ x⁶+a⁶ |+C

Step-by-step solution

Let I= x² x⁶+a⁶ d x Let x³=t aligned 3 x² d x &=d t I &= 1 3 1 t²+ (a³ )² d t &= 1 3 |t+ t²+a⁶ |+C &= 1 3 |x³+ x⁶+a⁶ |+C aligned

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