Finding indefinite integral ∫ DX / √ (e ^ 2x-1)

Finding indefinite integral ∫ DX / √ (e ^ 2x-1)

Let t = √ [e ^ (2x) - 1], T & # 178; + 1 = e ^ (2x), 2x = ln (T & # 178; + 1), DX = t / (1 + T & # 178;) DT ∫ DX / √ [e ^ (2x) - 1] = ∫ T / (1 + T & # 178;) * 1 / T DT = arctan (T) + C = arctan √ [e ^ (2x) - 1] + C

Seeking indefinite integral ∫ 2 ^ x * e ^ xdx

∫ 2^xe^x dx
=∫ (2e)^x dx
=(2e)^x/ln(2e) + C
=(2e)^x/(ln2+1) + C
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What is the indefinite integral of e ^ x ^ 2

This is not a product, there is no original function

Seeking indefinite integral ∫ 3 ^ x * e ^ xdx
Why is 3 ^ x * e ^ x equal to 3E ^ x?

Forget the above indefinite integral result, and finally add the constant C