# How do you evaluate the integral #int e^x/(root5(e^x-1))dx# from -1 to 1?

spotting the differentiation pattern, namely that :

we can say that

i'm not sure how more more that can be simplified

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To evaluate the integral (\int_{-1}^{1} \frac{e^x}{\sqrt{5(e^x - 1)}} dx), you can make the substitution (u = e^x - 1), which implies (du = e^x dx). The integral becomes (\int_{0}^{e-1} \frac{1}{\sqrt{5u}} du). This is a standard integral. You integrate (\frac{1}{\sqrt{5u}}) with respect to (u), then substitute back (e^x - 1) for (u), and evaluate the expression at the upper and lower limits of integration.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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