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How do you integrate #int (x^2(x^3 + 1)^3)dx#?

1 Answer

Konstantinos Michailidis

Oct 11, 2015

If we expand the product #x^2*(x^3+1)^3# we get

#x^11+3x^8+3x^5+x^2#

hence we have that

#int x^2(x^3+1)^3dx=int (x^11+3x^8+3x^5+x^2)dx=x^12/12+3*x^9/9+3*x^6/6+x^3/3=x^12/12+x^9/3+x^6/2+x^3/3+c#

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