Friday, March 18, 2022

March Calculus Madness Sweet Sixteen - Day 3: Derivative and Integral of x^n∙(1+x)^2

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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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