Question

$\int_{}^{}{x.(x^{x})^{x}}$ (2 log x + 1) dx

• A. $(x^{x})^{x}$ + c
• B. log (x)^x + c
• C. x^x + c
• D. None

Answer 1

Answer: (A)

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

Answer 2

Put $(x^{x})^{x}$ = t ̃ x log x^x = log t

̃ x² log x = log t

̃dx = $\frac{1}{t}$dt

̃ t (2 log x + 1) x dx = dt

̃ $\left( \mathrm { x } ^ { \mathrm { x } } \right) ^ { \mathrm { x } }$ (2 log x + 1) x dx = dt

so question becomes = $\int_{}^{}{1.dt}$= t + c