Question

$\int \frac{dx}{x.\left(inx\right)\left(in\right(inx\left)\right).......\frac{(ininin....inx)}{20times}}$ is equal to

• A. $\frac{(logloglog.....x)}{20times}+c$
• B. $\frac{(logloglog.....x)}{19times}+c$
• C. $\frac{(logloglog.....x)}{21times}+c$
• D. $\frac{(logloglog.....x)}{22times}+c$

Answer 1

The correct option is C $\frac{(logloglog.....x)}{21times}+c$

We have,

$\int \frac{dx}{x\left(\ln x\right)\left(\ln \left(\ln x\right)\right)........(\ln \ln \ln \ln x......\ln x)\left(20\text{times}\right)}$

Then,

We know that,

$\int \frac{dx}{x}=\ln x$

So, according to given question

$\int \frac{dx}{x\left(\ln x\right)\left(\ln \left(\ln x\right)\right)........(\ln \ln \ln \ln x......\ln x)\left(20\text{times}\right)}$

$\ln (x\ln x\left(\ln \left(\ln x\right)\right)........(lnlnlnlnx.....lnx)20\text{times})$

$\ln \ln \ln \ln x.....\ln x\left(21times\right)$

Hence this is the answer.