∫(dx/x⋅(ln x)(ln(ln x))....... ((ln ln ln ... ln x))20 times) is equal to

Question

∫(dx/x⋅(ln x)(ln(ln x))....... ((ln ln ln ... ln x))20 times) is equal to (A) ((log log log .....x)/20 times) +c (B) ((log log log .....x)/19 times) +c (C) ((log log log .....x)/21 times) +c (D) ((log log log .....x)/22 times) +c

Tardigrade Admin · Accepted Answer

Correct answer is (c) ((log log log .....x)/21 times) +c

Q. $\int \frac{d x}{x \cdot ( l n x ) ( l n ( l n x ) ) ....... \frac{( l n l n l n ... l n x )}{20 t im es}}$ is equal to

$\frac{( l o g l o g l o g ..... x )}{20 t im es} + c$

$\frac{( l o g l o g l o g ..... x )}{19 t im es} + c$

$\frac{( l o g l o g l o g ..... x )}{21 t im es} + c$

$\frac{( l o g l o g l o g ..... x )}{22 t im es} + c$

Correct answer is (c) $\frac{( l o g l o g l o g ..... x )}{21 t im es} + c$

Q. ∫x⋅(lnx)(ln(lnx)).......20times(lnlnln...lnx)​dx​ is equal to

20times(logloglog.....x)​+c

19times(logloglog.....x)​+c

21times(logloglog.....x)​+c

22times(logloglog.....x)​+c