∫$$ax2dxa$$−$$x+ax$$ is equal to

Correct option is 31logalogax+ax2+1+C

Questions

$\int \frac{a^{\frac{x}{2}} d x}{\sqrt{a^{- x} + a^{x}}} is equal to$

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logax+ax2+2+C

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1logalogax+ax2+1+C

1logalogax+ax2−1+C

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detailed solution

Correct option is C

Let I=∫ax2dxax2+1axI=∫ax2ax2dx(ax)2+1=∫axdx(ax)2+1 Put ax=t⇒axdx=1log⁡adtI=∫dtlog a1t2+1=1log⁡alog⁡t+t2+1+C=1log⁡alog⁡ax+ax2+1+C

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∫ax2dxa−x+ax is equal to

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$\int \frac{a^{\frac{x}{2}} d x}{\sqrt{a^{- x} + a^{x}}} is equal to$