WEBVTT
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All right, This question wants us to find the
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value of this integral. So to do this,
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we need to get it into one of the forms
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that our table needs. So we need to find
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a choice of you. So since we see a
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sign of ex inside of that natural log, that's
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probably a good guess. So look you equal to
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sign X. So that means set d'you is equal
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to co sign x d. X on we see
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, we do have a co sign there. Indeed
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. So are integral. Now becomes Thean Tha Gral
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of well, co sign next D X becomes d'you
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and then sign squared in front becomes you squared times
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the natural log of you, Do you now?
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This is something that are integral. Table can tell
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us what the value is. So it says,
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I'll just put this over here. The integral of
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you to the end. Ellen of you. Do
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you based on our formula is U to the n
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plus one over n plus one squared times n plus
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one Ellen of you minus one plus c so we
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can see that our inter girls just the n equals
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two case of this. So this is equal to
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you to the n plus one, which is three
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over and plus one squared times the natural log of
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n plus one times natural log of you minus one
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plus c. So then, if we look here
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, we get you cute. Over nine times three
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Ellen of you minus one. And now all we
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have to do is plug in. Are you value
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of sine X? So we get signed cube decks
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over nine times three natural log sine X minus one
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plus c and that's our final answer.