WEBVTT
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Okay, so this question wants us to integrate this
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function. So to do that, we need to
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transform it into one of the forms we can see
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in our table. So to do this, we
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always like to see a U squared insider square roots
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. So let's pick you to be equal to eat
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of the ex. So that means that do you
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is equal to eat of the ex DX. But
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we don't have that anywhere. So we need to
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divide by e to the X. So we get
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do you overeat of the ex is equal to D
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X So now we can transform. This is the
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integral of square root eat of the two x you
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squared minus one divided by archangel factor of e to
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the X Do you? But we can't keep this
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eat of the X in that form We need to
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change the u world now So either the axe is
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equal to you Then X equals the natural law give
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you so we can rewrite. This is the integral
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the square root of you squared minus one over e
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to the Ellen of you. Do you? Which
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is equal to well, he's to cancel, and
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this is an integral we can compute. We just
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look at the following formula from our table and in
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this case, a equals one. So that makes
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are integral square root. You squared minus one minus
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co sign in verse a over absolute belly of you
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plus c them plugging back in. We'll get our
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final answer of each of the two X minus one
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minus co. Sign in verse of one over absolute
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value of E to the X, which is just
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eat of the ex because either the exes always positive
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plus c giving us our final answer.