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Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeAnswer (1 of 5) For certain real numbers a, b, and c, the polynomial g(x) =x^3 ax^2 x10 has three distinct roots, and each root of g(x) is also a root of theIntegration by Substitution Let u = g(x) and F(x) be the antiderivative of f(x) Then du = g0(x)dx and Z f g(x) g0(x)dx = Z f(u)du = F(u)C Also, Z b a f g(x) g0(x)dx = Z g(b) g(a) f(u)du = F g(b) −F g(a) Ex u = g(x) = x2, du = g0(x)dx = 2xdx Z 5 2 2xex2dx = Z 52=25 22=4 eu du = eu 25 4 = e25 −e4 Integration Rules Examples Z kdu = kuC Z



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