Cute calculus : Problem no.1

Calculus Level pending

If \(\displaystyle\large\int { f\left( x \right) dx=F\left( x \right) } \). Then \(\displaystyle \large \int { { x }^{ 3 } } f\left( { x }^{ 2 } \right) dx\) is equal to :

A) \(\displaystyle \cfrac { 1 }{ 2 } \left[ { x }^{ 2 }{ F\left( { x }^{ 2 } \right) }-\int { F\left( { x }^{ 2 } \right) d\left( { x }^{ 2 } \right) } \right] \)

B) \(\displaystyle \cfrac { 1 }{ 2 } \left[ { x }^{ 2 }{ \left\{ F\left( x \right) \right\} }^{ 2 }-\int { { \left\{ F\left( x \right) \right\} }^{ 2 }dx } \right] \)

C)\(\displaystyle \cfrac { 1 }{ 2 } \left[ { x }^{ 2 }F\left( x \right) -\cfrac { 1 }{ 2 } \int { { \left\{ F\left( x \right) \right\} }^{ 2 }dx } \right] \)

D) None Of These

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