What is $int (lnsqrt(3x+2))^2dx$ ?

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Answer 1 · 2015-11-02T18:46:55

Here is some help to get you started.

$int (lnsqrt(3x+2))^2dx$

Let's look at the integrand for a bit:

$(lnsqrt(3x+2))^2$

First note that $(lnsqrt(3x+2)) = ln(3x+2)^(1/2) = 1/2ln(3x+2)$

and $3x+2$ is linear, so we can do a substitution.

Then the question will be how to find

$int (lnt)^2 dt$

Details

$int(lnsqrt(3x+2))^2dx = int (1/2ln(3x+2))^2 dx$

$= 1/4 int (ln(3x+2))^2 dx$

With $t = 3x+2$ , the integral becomes:

$= 1/12 int (lnt)^2 dt$

Now try substitution, try parts, try anything else you think of.

Hint
Recall that we can integrate $lnx$ by using integration by parts.

What is int (lnsqrt(3x+2))^2dxint (lnsqrt(3x+2))^2dx?