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Okay, This question wants us to evaluate the integral
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of C can't x to the fifth power. So
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to do this, we consult our formula for seeking
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to the end anti derivative. So all we gotta
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do is apply the formula. So if an equals
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five says that this is equal to tangent X c
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can't to the and minus two, divided by n
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minus one plus and minus two over and minus one
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times the integral of C can't to the n minus
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two d x. And then we can use the
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same formula again to analyze, seek and cubed vex
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. So in a girl of C can't cubed iss
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tan axe c can't of n minus two, which
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is just the first power over and minus one plus
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and minus two over and minus one times the integral
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of C can't to the n minus two. And
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we actually know the internal of C can't to the
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first power, which is Ellen of Seek an X
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plus Tangent acts. So now let's back substitute everything
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in. So our final integral of seek and to
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the fifth I'm just gonna do a little box over
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here because we need a lot of space tangent X
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c can't huge x over four plus 3/4 times are
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integral of C can't cubed, which is tan axe
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. Seek an axe over too, plus 1/2 Ellen
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of Seek an Axe plus Tangent X Plus C,
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of course. And if we do all the math
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and simplify our fractions here, we get the following
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plus 3/4 times. 1/2 is 3/8 and that 3/8
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is also attached to our log term. And we
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have our integration constant so again only had to do
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was applied. The sea can't formula over and over
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again.