Mathematics: Finding an indefinite integral dx/x(lnx^2)^3

Finding an indefinite integral dx/x(lnx^2)^3

alayciaruffin076

10.03.2022

Step-by-step explanation:

Firstly, we'll try to simplify the integrand. By hint 1, we see that:

$\ln(x^2) = 2\ln(x)$

Simplifying the integrand gives us:

$\frac{1}{8}\left(\frac{1}{x(\ln(x))^3}\right)$

Next, by hint 2, we observe that:

$\frac{d}{dx}\left(\ln(x)\right) = \frac{1}{x}$

So this tells us to make the substitution: $u = \ln(x)$

Doing so gives us:

$\int \frac{dx}{x(ln(x^2))^3} = \int \frac{du}{8u^3}$ , which should be trivial.

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130005401

31.12.2021

is the a b c and d the answer chooses? ill be able to answer it once i know

Step-by-step explanation:

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