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Combining the pairs of conjugate partial fractions according to equation (29), the first pair becomes

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and similarly will the other pairs of conjugate partial fractions be compounded; so that the following series will be formed,

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If n is even, then equation (48), by means of Art. 64, Vol. I,

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1

= log(-1) + cos log (-2.rcos 27+1)

1

3

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COS
3 3

2 2π

x

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= log(x
log (x − 1) — log (x2 + x + 1) −√

6

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Let n be even; then, in Art. 65, Vol. I, it is proved that the

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and combining the pairs of conjugate partial fractions, according to equation (29), the first pair is

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and the other pairs give similar results; so that

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each of which must be integrated according to the process in

dicated in the preceding article.

Again, let n be odd: then the roots of "+1 = 0 are

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so that if the conjugate partial fractions are combined by a process similar to that employed when n is even, the last pair becomes

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1

x2

1 π
sintan

= cos log (a2-22 cos+1) + sin tan-1.

π

4

2

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π

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1

3п.

4

cos log (-2rcos+1)+ sin tan

3 п

COS4

-1

4

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