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Definite Integration question

2022 · 28 Jul · Shift 1 · Q41

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 28 Jul · Shift 1 · Q41

Definite Integration question

2022 · 28 Jul · Shift 1 · Q41

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

If

\int\limits_{0}^{\sqrt{3}} \frac{15 x^{3}}{\sqrt{1+x^{2}+\sqrt{\left(1+x^{2}\right)^{3}}}} \mathrm{~d} x=\alpha \sqrt{2}+\beta \sqrt{3}

, where

\alpha, \beta

are integers, then

\alpha+\beta

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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