WEBVTT
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this problem is from Chapter seven section to problem number
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fourteen in the book Calculus Early Transcendence. ALS eighth
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edition, My James Door Here we have a indefinite
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integral of sine squared of one over t all divided
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by t squared. So before we start integrate here
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, we can apply u substitution. Let's take you
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two be one over tea so that to you using
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the powerful from differential calculus is negative. One over
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T square dt equivalently negative to you is one over
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teeth clear. Titi. So if we apply our
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u substitution here, we can rewrite our original integral
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as negative in a girl Signed square of you Deal
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Now we can apply an identity for science where using
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a trick in a metric identity. Let's re write
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this expression here the inside rent We have integral negative
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in general and we can rewrite this sign square as
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one minus co sign off to you all divided by
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two. And now we could integrate each of these
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two terms And for the second term am I helped
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to use another use of and the integration you could
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take. Let's stay here W since we're already using
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you for a previous use up here. You could
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use another letter w for your other u sub and
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you could take that to be to you so integrating
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each of these terms. So in a girl,
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one over two becomes you over, too. And
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for the second, integral, we have a negative
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sign of to you over two times two, which
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is for and our constant of integration seat. So
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we have two steps left. We can distribute the
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negative sign and through the parentheses. And we could
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also replace you with one oversee. So, doing
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both of these Ted step simultaneously. We have negative
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one over Tootie, plus sign of two over tea
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over floor, plus see, and that's your final
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answer.