Integrate the function frac{(log x)^{2}}{x}. | vedclass

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(A) Let $\log x = t$. Then,differentiating with respect to $x$,we get $\frac{1}{x} dx = dt$. Substituting these into the integral,we have: $\int \frac

Vedclass · Accepted Answer

$\frac{(\log x)^{3}}{3} + C$

Vedclass · Answer

(A) Let $\log x = t$. Then,differentiating with respect to $x$,we get $\frac{1}{x} dx = dt$. Substituting these into the integral,we have: $\int \frac{(\log x)^{2}}{x} dx = \int t^{2} dt$. Using the power rule for integration $\int x^{n} dx = \frac{x^{n+1}}{n+1} + C$,we get: $\int t^{2} dt = \frac{t^{3}}{3} + C$. Substituting $t = \log x$ back into the expression,we obtain: $\frac{(\log x)^{3}}{3} + C$,where $C$ is an arbitrary constant.

Integrate the function $\frac{(\log x)^{2}}{x}$.

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