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KCET2021MathematicsIndefinite Integration

x³ ( ⁻¹ (x⁴ ) ) 1+x⁸ d x is equal to

Options

  1. A- ( ⁻¹ (x⁴ ) ) 4 +C
  2. B( ⁻¹ (x⁴ ) ) 4 +C
  3. C- ( ⁻¹ (x³ ) ) 3 +C
  4. D( ⁻¹ (x⁴ ) ) 4 +C

Correct answer

A. - ( ⁻¹ (x⁴ ) ) 4 +C

Step-by-step solution

Let I= x³ [ ⁻¹ (x⁴ ) ] 1+x⁸ Let ⁻¹ (x⁴ )=t . On differentiating w.r.t. t , we get gathered 1 1+x⁸ 4 x³ d x=d t x³ 1+x⁸ d x= 1 4 d t I= 1 4 t d t gathered =- 1 4 t+C=- 1 4 ( ⁻¹ (x⁴ ) )+C

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