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  • How to solve this problem- - Integral Calculus - JEE Main-5

If \int \frac{e^{x}\left ( 2-x^{x^{2}} \right )}{\left ( 1-x \right )\sqrt{1-x^{2}}}dx=\mu e^{x}\left (\frac{1+x}{1-x} \right )^{\lambda }+c\: ,then \: \lambda +\mu =

  • Option 1)

    5/2

  • Option 2)

    2

  • Option 3)

    3/2

  • Option 4)

    1/2

 

Answers (1)

As we learnt

Result for integration by parts -

\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c

- wherein

It works on integration by parts of  \int e^{x}f\left ( x \right )dx

 

 

I = \int {{e^x}} \left( {\frac{1}{{\left( {1 - x} \right)\sqrt {1 - {x^2}} }} + \sqrt {\frac{{1 + x}}{{1 - x}}} } \right)dx

As\: \frac{d}{{dx}}\left( {\sqrt {\frac{{1 + x}}{{1 - x}}} } \right) = \frac{1}{{\left( {1 - x} \right)\sqrt {1 - {x^2}} }}

\therefore I = {e^x}\sqrt {\frac{{1 + x}}{{1 - x}}} + c


Option 1)

5/2

Option 2)

2

Option 3)

3/2

Option 4)

1/2

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