Combining the pairs of conjugate partial fractions according to equation (29), the first pair becomes and similarly will the other pairs of conjugate partial fractions be compounded; so that the following series will be formed, Let n be even; then, in Art. 65, Vol. I, it is proved that the roots of a*+1 are cos±√lsin, 3п 3п COS +V-1sin , n n roots of "+1 = 0; therefore the coefficient and combining the pairs of conjugate partial fractions, according to equation (29), the first pair is and the other pairs give similar results; so that 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 so that if the conjugate partial fractions are combined by a process similar to that employed when n is even, the last pair becomes |