If $$I=$$∫$$dx2ax+x23/2$$, then I is equal to

Correct option is 3−1a2x+a2ax+x2+C

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$If I = \int \frac{d x}{{(2 a x + x^{2})}^{3 / 2}}, then I is equal to$

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detailed solution

Correct option is C

Write 2ax+x2=(x+a)2−a2, and put x+a=asec⁡θ, so that dx=asec⁡θtan⁡θdθ∴I=∫asec⁡θtan⁡θa3tan3⁡θdθ=1a2∫cos⁡θsin2θdθ=−1a2sin⁡θ+C=−1a2sec⁡θtan⁡θ+C=−1a2x+a2ax+x2+C

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If I=∫dx2ax+x23/2, then I is equal to

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$If I = \int \frac{d x}{{(2 a x + x^{2})}^{3 / 2}}, then I is equal to$