Mathematics

Evaluate 
$$\int \dfrac{\log (1+x)}{(1+x)}dx$$


SOLUTION
$$\begin{array}{l} \int { \dfrac { { \log  \left( { 1+x } \right)  } }{ { 1+x } } dx }  \\ u=\log  \left( { 1+x } \right) \, \, \, \, du=\dfrac { 1 }{ { 1+x } } dx \\ \int { u\, \, du=\dfrac { { { u^{ 2 } } } }{ 2 } +c }  \\ =\dfrac { 1 }{ 2 } { \left( { \log  \left( { 1+x } \right)  } \right) ^{ 2 } }+c \end{array}$$

Hence, this is the answer.
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Subjective Hard Published on 17th 09, 2020
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