Indefinite IntegrationHard

Question

The value ofdx is equal to

Options

A.
B.
C.
D.

Solution

dx    put √x = cos 2t ⇒ dx = - 4 sin 2t cos 2t dt
= (- 4 sin 2t cos 2t) dt
= . 2sin t cos t cos 2t . dt
= - 4∫(1 - cot2t) cos 2t dt
= - 4∫cos2t dt + 4∫cos22t dt
= - 2 sin 2t + 2 × + 2t + C
= - 2 + √x+ cos-1 √x + C

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