How do you integrate $(5)/(1+3x)^3$ ?

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Answer 1 · 2015-08-23T12:18:39

The answer is $-5/(6(1+3x)^2)$

Rewrite as : $5/3int3/(1+3x)^3dx$

Now let's : $u = 1+3x$
then $du = 3$

So we have :

$5/3int1/u^3du = 5/3intu^(-3)du$

$=> 5/3[-1/2u^(-2)] = -5/6[1/u^2]$

Dont forget $u = 1+3x$

Finally : $-5/(6(1+3x)^2)$

How do you integrate (5)/(1+3x)^3(5)/(1+3x)^3?