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Welcome to March Calculus Madness!
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x^n ∙ (1 + x)^2
= x^n ∙ (1 + 2 ∙ x + x^2)
= x^n + 2 ∙x^(n+1) + x^(n+2)
d/dx x^n ∙ (1 + x)^2
= d/dx x^n + 2 ∙x^(n+1) + x^(n+2)
= n ∙ x^(n-1) + 2 ∙ (n+1) ∙ x^n + (n+2) ∙ x^(n+1)
∫ x^n ∙ (1 + x)^2 dx
= ∫ x^n + 2 ∙x^(n+1) + x^(n+2) dx
= x^(n+1)/(n+1) + (2 ∙ x^(n+2))/(n+2) + x^(n+3)/(n+3) + C
Eddie
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