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If you are calculating Integral ((x^3+2)^2* 3x^2*dx) define X=x^3+2, dX=3.x^2 dx, integral becomes Integral (X^3.dX)=X^3/3=(1/3)(x^3+2)^3
If you are calculating Integral ((x^3+2)^2* 3x^4*dx), develop the binomial, and use the rule for the integral of a power to integrate each term in the polynomial of degree 10 that you obtain. I will leave this for you to do.