Question

integrate the function (1 + logx)²/x

Answer 1

HELLO DEAR,

GIVEN function is $\bold{\int{(1 + logx)^2/x}\, dx}$

let logx = t
$\bold{\Rightarrow 1/x = dt/dx}$
$\bold{\Rightarrow dx = xdt}$

so, $\bold{\Rightarrow \int{(1 + t)^2/x}\,xdt}$

$\bold{\Rightarrow \int{(1 + t)^2}}$

$\bold{\Rightarrow \int{(1 + t^2 + 2t)}\,dt}$

$\bold{\Rightarrow (t + t^3/3 + t^2) + c}$.

put the value of t in above function

$\bold{\Rightarrow logx[1 + (logx)^2 /3 + logx] + C}$

I HOPE ITS HELP YOU DEAR,
THANKS
I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hope it will help you!!