Mathematics

# The value of $\int _{ 0 }^{ \pi /4 }{ \dfrac { 1+\tan { x } }{ 1-\tan { x } } } dx$ is

##### SOLUTION
$\begin{array}{l} \int _{ 0 }^{ \frac { \pi }{ 4 } }{ \frac { { \left( { 1+\tan x } \right) } }{ { \left( { 1-\tan x } \right) } } dx } \\ \Rightarrow \int _{ 0 }^{ \frac { \pi }{ 4 } }{ \tan \left( { \frac { \pi }{ 4 } +x } \right) dx } \\ \Rightarrow -\left[ { \log \left| { \cos \left( { \frac { \pi }{ 4 } +x } \right) } \right| } \right] _{ 0 }^{ \frac { \pi }{ 4 } }+c \\ \Rightarrow -\log \left| { \cos \frac { \pi }{ 2 } -\cos \frac { \pi }{ 4 } } \right| +c \\ \Rightarrow -\log \left| { -\frac { 1 }{ { \sqrt { 2 } } } } \right| +c \\ \Rightarrow -\log { 2^{ \frac { { -1 } }{ 2 } } } +c \\ \frac { 1 }{ 2 } { \log { 2 } }+c \end{array}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
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