Can someone explain in detail how to solve the below indefinite integral? I am getting really...

Can someone explain in detail how to solve the below indefinite integral? I am getting really confused when it comes to the U-substitution part and do not understand how 9 ends up in the denominator.

I know the correct answer is [-2(ln3x+1)-3x]/9 + C, but I do not know how to get there.

∫(2x)/(3x+1) dx

Expert Solution

let, I = che 3xt I 2 2 30 3x+1 dre 2 33 32 + 1 - 1 dhe 30t1 I= 33 [S 3x+1 30ti da Sveti dse 3x + 1 . I = 2 3 [sinde [ s got7 de 30t :: I - 2 [ X - 3 In (3x+1) d (3x + 1) 6] +C (s to che dro en fex ) d f (c) doc I= dlm 20 en (3x+1) tc 3 I = WIN 2 ln c3x+ 1) 3x3 C I = 2 w/P 2 en 3x+1) 9 tc

milcah answered 2 years ago

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Can someone explain in detail how to solve the below indefinite integral? I am getting really...

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