integration

if i integrate 36/(2x+1)^4 ,

i do: 36(1/(2x+1)^4 /2
= 18 ln(2x+1)4 + c. is this right?

if i integrate 36/(2x+1)^4 ,

i do: 36(1/(2x+1)^4 /2
= 18 ln(2x+1)4 + c. is this right?

It's not a case of natural logs because the denominator has a power of 4 and not 1 i.e.

\int\frac{1}{2x+1}dx

becomes a natural log because the denominator is

(2x+1)^{1}

The question is a simple case of integration actually,

36\int\frac{1}{(2x+1)^{4}}dx \Rightarrow 36\int(2x+1)^{-4}dx

you can change the variable:

let u = 2x + 1

du/dx = 2

dx = du/2

∫ 36u^-4/2 du

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