Question

Solve :

$\int x.\left(x^x{)}^x\right(2\log x+1)dx$

• A. $x^{\left(x^x\right)}+c$
• B. $(x^x{)}^x+c$
• C. $x^x.\log x+c$
• D. does not exist

Answer 1

Answer: (B)

$(x^x{)}^x+c$

$\int x.\left(x^x{)}^x\right(2\log x+1)dx$
Put $(x^x{)}^x=t$
$x\log x^x=\log t$
$x^2\log x=\log t$
$\Rightarrow x(1+2\log x)dx=\frac{1}{t}dt$
So,$I=\int t\left(\frac{1}{t}\right)dt$
$=\int dt$
$=t+C$
$I=(x^x{)}^x+C$