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\int_{-1/2}^{1/2}cosx \, ln\left ( \frac{1+x}{1-x} \right )dx

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As we learnt

Properties of Definite Integration -

If f(x) is an odd function of x then integral of the function from -a to a is ZERO

\int_{-a}^{a}f(x)dx=0
 

- wherein

Check

Odd function f(-x)= -f(x)

 

 

 

f(-x)=cos(-x)ln\left ( \frac{1-x}{1+x} \right )=-cosxln\left ( \frac{1-x}{1+x} \right )=-f(x)\therefore f(x)\; is\; odd

                        Hence, the value of the given integral = 0.

 

 


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Option 3)

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Option 4)

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