Question

please give me the answer with explaination​

Answer 1

Step-by-step explanation:

$\tt \int log(x+1)\:dx \\ \\ \tt Let\: x + 1 = t \\ \\ \tt Differentiating \: on \: both \: sides \\ \\ \tt dx = dt \\ \\ \tt \longrightarrow \int log t \: dt \\ \\ \tt Using \: by \: parts \\ \\ \tt Let\:u=logt \: \: \: v = 1 \\ \\ \tt \longrightarrow logt \int 1 dt - \int \frac{d(logt)}{dt} \int 1 dt \\ \\ \tt \longrightarrow logt . t- \int \frac{1}{t} . t \: dt \\ \\ \tt \longrightarrow tlogt - \int 1 dt \\ \\ \tt \longrightarrow tlogt - t + c \\ \\ \tt \longrightarrow (x+1)log(x+1) - (x+1) + c\\ \\ \tt \longrightarrow \boxed{\bold{\red{\tt \int log{x}^{2} = (x+1)log(x+1) - (x+1) + c }}}$