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Factor out the constant and use power rule :

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This question is type of

integration X^n dx= x^n+1/n+1 +c where c is arbitrary const.

integration 12 x^7/2 dx

12 integration

7/2 +1

integration

9/2

integration X^n dx= x^n+1/n+1 +c where c is arbitrary const.

integration 12 x^7/2 dx

12 integration

__x^7/2 +1__no effect on constant during7/2 +1

integration

__12 x^9/2__⇒8/3 x^9/2 +c9/2