1on seeing the limits , the natural instinct is to put 1x=t
and then proceed
$Calculate $\int_{\frac{1}{2}}^{2}\frac{1}{(x^2-3x).(x^{2010}+1)}dx$
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3 Answers
1
1708$Extremely Sorry for posting a Wrong Integral.....\\\\ The Righta Integral is $\int_{\frac{1}{2}}^{2}\frac{1}{(3x^2-10x+3)(x^{2010}+1)}dx$
1I=\int_{\frac{1}{2}}^{2}{\frac{dx}{(3x-1)(x-3)(1+x^{2010})}}
t=\frac{1}{x}
now u get
I=\int_{\frac{1}{2}}^{2}{\frac{t^{2010}dt}{(3t-1)(t-3)(1+t^{2010})}}
2I=\int_{\frac{1}{2}}^{2}{\frac{dx}{(3x-1)(x-3)}}
this can be done easily
Ans=-\frac{\ln(25)}{16}