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Integrate dx/{(1+vx).v(x-x^2)}= 2(vx-1)/ v(1-x) + c

Integrate

dx/{(1+vx).v(x-x^2)}=
2(vx-1)/ v(1-x) + c

Grade:12th Pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
This can be done by the partial fraction rule.
I = \int \frac{dx}{v.(vx+1)(x-x^{2})}
I = \int \frac{dx}{v.(vx+1)x(1-x)}
I = \frac{1}{v}\int (\frac{1}{x}+\frac{\frac{1}{v+1}}{1-x}+\frac{\frac{-v^{2}}{v+1}}{vx+1})dx
I = \frac{1}{v}[lnx-\frac{1}{v+1}ln(1-x)-\frac{v}{v+1}ln(vx+1)]+c
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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