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Definite Integration question

2015 · Shift 2 · Q39

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2015 · Shift 2 · Q39

Definite Integration question

2015 · Shift 2 · Q39

JEE AdvancedMathematicsDefinite IntegrationNumerical+4 / −1

If

\alpha = \int\limits_0^1 {\left( {{e^{9x + 3{{\tan }^{ - 1}}x}}} \right)\left( {{{12 + 9{x^2}} \over {1 + {x^2}}}} \right)} dx

where

{\tan ^{ - 1}}x

takes only principal values, then the value of

\left( {{{\log }_e}\left| {1 + \alpha } \right| - {{3\pi } \over 4}} \right)

is

Numerical answer

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