WEBVTT
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Okay. This question wants us to integrate this function
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. Using a table so well, usually like,
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is having some sort of a you squared in the
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denominator. So let's have you equal eat of the
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ex. So that means that do you equals you
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to the x d x. But we don't have
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any of those. So do you. Over e
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to the X equals DX. So no, we
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can write this as d'you over either the X square
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roots one minus you squared. But we're still not
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done because we haven't eat of the ex and we're
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supposed to be in the u world. So if
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you is equal to eat of the X, then
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X is equal to Ellen of you. So now
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we can rewrite this as the integral of D'You over
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E to the Ellen of you Square group one minus
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you squared and we see the deed to the Ellen
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. You is just you. So we get our
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final integral of d U. Over you square root
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one minus you squared. And this is something that
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we can look up in our table. It's exactly
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one of the forms. So we get that this
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is equal to negative times. Ln of absolute value
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, one plus square root one minus You squared all
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over you plus C And now we can flip this
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fraction over and put them to get rid of the
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negative sign. So we get equals. Ellen of
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you over one plus square, one minus you squared
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plus c. And then the last thing we got
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to d'oh is plug in eat of the ex for
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you and now we're done.