Question

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

• A. $\frac{(\log x{)}^2}{2}+c$
• B. $\frac{(\log x{)}^3}{3}+c$
• C. $\frac{(\log x{)}^4}{2}+c$
• D. $\frac{(\log x{)}^5}{3}+c$

Answer 1

Answer: (B)

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

$\int \frac{lo{g}^{2}x}{x}dx$.

put $logx=t$ ....... (1)

Therefore, $\frac{1}{x}.dx=dt$

=> $\int t^{2}dt$.

=> $\frac{t^3}{3}+C$

Put value of $t$ from eq. (1).

we get,

=> $\frac{(logx{)}^3}{3}+C$