If I n -ln x n d xthen I n - nI n -1A- ln xnB- xln xn-1C- None of these D- xln xn

The correct option is D x (ln x)^n I_n=x(ln x)^n ∫x(n)(ln x)^n 1/xdx =x(ln x)^n nI_(n 1) ⇒ I_n+nI_n 1=x(ln x)^n ...

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Integration of Trigonometric Functions

If I n =∫ln x...

Question

If $I_{n} = \int (l n x)^{n} d x t h e n I_{n} + n I_{n - 1}$

$\frac{(l n x)^{n}}{x}$

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$x (l n x)^{n - 1}$

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$x (l n x)^{n}$

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None of these

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Solution

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(2^{n} + 1) θ = π,

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(2^{n} + 1) x = π,

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f (x) = \frac{\sqrt{x - 1}}{\sqrt{x - 1}}

f (x) = x + \frac{1}{x} + 1

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