E6: Integrals of the form (a^2-x^2)^(-½) and (a^2+x^2)^(-1)

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From the DfE Mathematics AS and A-Level Further Maths Content (LINK):

PLAYLIST

Integrating to arcsin(x) & arctan(x)

E6-01 Further Integration: Integrating (1-x^2)^(-½)

E6-02 Further Integration: Integrating (1+x^2)^(-1)

E6-03 Further Integration: Integrals of the form (a^2-x^2)^(-½) and (a^2+x^2)^(-1)

E6-04 Further Integration: Integrating (1+(x^2)/9)^(-1)

E6-05 Further Integration: Integrating (25 - 3x^2)^(-½)

E6-06 Further Integration: Definite Integral Example

E6-07 Further Integration: More Examples