Question

please solve and keep with explaination​

Answer 1

Step-by-step explanation:

$\tt \int log {x}^{2} \:dx \\ \\ \tt \longrightarrow \int 2 log x \: dx \\ \\ \tt Using \: by \: parts \\ \\ \tt Let\:u=logx \: \: \: v = 2 \\ \\ \tt \longrightarrow logx \int 2 dx - \int \frac{d(logx)}{dx} \int 2 dx \\ \\ \tt \longrightarrow logx . 2x - \int \frac{1}{x} . 2x \: dx \\ \\ \tt \longrightarrow 2xlogx - \int 2 dx \\ \\ \tt \longrightarrow 2xlogx - 2x + c \\ \\ \tt \longrightarrow \boxed{\bold{\red{\tt \int log{x}^{2} = 2xlogx - 2x + c }}}$