Integrate 2x(x^2-1)^5 dx

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Question from joey, a student:

pls help me to integrate
2x(x^2-1)^5 dx using the substitution u=x^2-1

Hi Joey,

If you use the substitution u = x² - 1 then du = 2x dx so the integrand becomes

u⁵ du

Can you complete it now. You can check your answer by differentiating it to see if you get 2x(x²-1)⁵

Harley

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