# How do you find the integral of #e^(2x) sqrt(1 + e^(2x)) dx#?

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To find the integral of ( e^{2x} \sqrt{1 + e^{2x}} , dx ), you can use a substitution. Let ( u = 1 + e^{2x} ). Then, ( du = 2e^{2x} , dx ). Rearrange this to get ( dx = \frac{1}{2e^{2x}} du ). Now, substitute ( u ) and ( dx ) into the integral. You will have ( \frac{1}{2} \int u^{1/2} , du ). Integrate ( u^{1/2} ) with respect to ( u ), then substitute back ( e^{2x} ) for ( u ) to get the final result.

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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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