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Choose the correct option.
If ∫ ((log x)²)/x dx = ((log x)^k)/k + c, then the value of k is:
If $\int \frac{(\log x)^2}{x} \, dx = \frac{(\log x)^k}{k} + c$, then the value of $k$ is:
- (a)3
- (b)2
- (c)1
- (d)None of the above options
Answer
Answer
Correct option: (a)
Answer: (a) 3
Put $\log x = t$, so $\frac{dx}{x} = dt$.
$\int t^2\,dt = \frac{t^3}{3} + c = \frac{(\log x)^3}{3} + c$, hence $k = 3$.