How do you integrate f(x)=(2+x+2x^2-3x^3)(3-x+2x^2+2x^3) using the product rule?

1 Answer
Dec 25, 2017

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Explanation:

If 2+x+2x^2 -3x^3 =g(x) and 3-x+2x^2+2x^3= h(x), then int g(x)*h(x) dx=g(x) int h(x)dx - int d/dx g(x) int h(x)dx. Accordingly,

int g(x)*g(x) dx= (2+x+2x^2-3x^3)(3x-x^2/2 +2 x^3 /3 +2x^4 /4) -int (1+4x-9x^2)(3x-x^2/2 +2 x^3 /3 +2x^4 /4)dx

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