Question

Integrate the following function with respect to $x$
$\frac{(x+1).(x+\log x{)}^4}{3x}$

Answer 1

According to question,

Let,

$x+logx=t$

$⟹(1+\frac{1}{x})dx=dt$

$⟹\left(\frac{1+x}{x}\right)dx=dt$

Substitute this values, we get

$\int \frac{t^4}{3}dt$

$⟹\frac{t^5}{3\times 5}+C$

$⟹\frac{(x+logx{)}^5}{15}+C$