If $\int f(x) d x=F(x)$, then $\int x^3 f\left(x^2\right) d x$ is equal to

• A

  $\frac{1}{2}\left[x^2\{F(x)\}^2-\int\{F(x)\}^2 d x\right]$
• Correct answer
  B

  $\frac{1}{2}\left[x^2 F\left(x^2\right)-\int F\left(x^2\right) d\left(x^2\right)\right]$
• C

  $\frac{1}{2}\left[x^2 F(x)-\frac{1}{2} \int\{F(x)\}^2 d x\right]$
• D

  None of the above

Hence, the correct answer is option: 'B'.