( viii ) Form VIII
( ix ) Form IX
To evaluate the above type of integrals , we proceed as follows
Divide numerator and denominator by x 2
Express the denominator of integrands in the form of ( x + 1 / x ) 2 ± k 2 Introduce ( x + 1 / x ) or d ( x – 1 / x ) or both in numerator . Put x + 1 / x = t or x – 1 / x = t as the case may be .
Integral reduced to the form of ∫ 1 / x 2 + a 2 dx or ∫ 1 / x 2 + a 2 dx
( x ) Form X