Question

Plsss solve this asap!

Answer 1

Let $\large\rm{ I = \displaystyle{\int} \rm{\dfrac{(\log \ x)^{2}}{x} dx}}$

$\large\rm$

$\large\rm{ \log \ x = t \implies \dfrac{dx}{x} = dt}$

$\large\rm$

$\large\rm{ I = \displaystyle\int \rm{ t^{2} \ dt}}$

$\large\rm$

$\large\rm{ I = \dfrac{t^{3}}{3} + C}$

$\large\rm$

$\large\rm{ I = \dfrac{( \log \ x)^{3}}{3} + C}$

$\large\rm$

$\large\rm{ = \dfrac{1}{3} ( \log \ x)^{3} + C}$

$\large\rm$

so 1st option is correct.

Answer 2

Answer:

Optiona correct

Step-by-step explanation:

Correc