KCET2021MathematicsIndefinite Integration
x³ ( ⁻¹ (x⁴ ) ) 1+x⁸ d x is equal to
Options
- A- ( ⁻¹ (x⁴ ) ) 4 +C
- B( ⁻¹ (x⁴ ) ) 4 +C
- C- ( ⁻¹ (x³ ) ) 3 +C
- 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