Evaluate the following integral:

Denominator is factorized, so let separate the fraction through partial fraction, hence let







By equating similar terms, we get


A + C = 0 A = – C ………..(iii)


B + D = 1 B = 1 – D…………(iv)


25A + 4C = 0


25( – C) + 4C = 0 (from equation(iii))


C = 0………..(v)



So equation(iv) becomes


So equation (iii) becomes, A = 0


We put the values of A, B, C, and D values back into our partial fractions in equation (i) and replace this as the integrand. We get





Split up the integral,



Let substitute


in first partthe


in second parthe t


so the above equation becomes,





On integrating we get



(the standard integral of )


Substituting back, we get



Note: the absolute value signs account for the domain of the natural log function (x>0).


Hence,



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