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$\int \frac{e^{x}}{2 e^{2 x} + 3 e^{x} + 2} d x is equal to$

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detailed solution

Correct option is C

∫ex2e2x+3ex+2dx Put ex=texdx−dt∫exex2+3ex+2dx=∫dtt2+3t+2=∫dtt2+232t+322−322+2 Use ∫1x2−a2dx=12alog⁡x−ax+a+c=∫dtt+322−122=12⋅12log⁡t+32−12t+32+12+k=log⁡2ex+22ex+4+k=log⁡ex+1ex+2+k

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∫ex2e2x+3ex+2dx is equal to

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$\int \frac{e^{x}}{2 e^{2 x} + 3 e^{x} + 2} d x is equal to$