( 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