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The integral \({\int }_{0}^{\frac{\pi }{4}}\frac{136\sin x}{3\sin x+5\cos x}dx\) is equal to : [JEE Main 2024, 5 Apr (Sh…

Q1

The integral \({\int }_{0}^{\frac{\pi }{4}}\frac{136\sin x}{3\sin x+5\cos x}dx\) is equal to :

[JEE Main 2024, 5 Apr (Shift 1)]

a

\(3\pi -30{\log }_{e}2+20{\log }_{e}5\)

b

\(3\pi -10{\log }_{e}(2\sqrt{2})+10{\log }_{e}5\)

c

\(3\pi -25{\log }_{e}2+10{\log }_{e}5\)

d

\(3\pi -50{\log }_{e}2+20{\log }_{e}5\)

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