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Question

 

∫(6x-1)⁵ dx=

Answer 1

You could multiply out the polynomial and then integrate term by term, but it's easier to do a u-substitution  

 

Let u = 6x - 1

Then du = 6dx  ==>  dx = du/6 

 

∫(6x-1)⁵dx = ∫(1/6)u⁵du = (1/6)u⁶/6 + C = (1/36)(6x-1)⁶ + C 

 

You can check the answer by taking the derivative which is 

 

6(1/36)(6x-1)⁵(6) = (6x-1)⁵