Question

Integration of 1+v/1-2v-v^2 dV

Answer 1

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Answer 2

Answer:

Let I=∫1+v1−2v−v2dv

=∫1+v2−1−2v−v2dv

=∫1+v2−(v+1)2dv

=∫2(1+v)2(2–√−v−1)(2–√+v+1)dv

=∫12(2–√−v−1)dv−∫12(2–√+v+1)dv

=−ln(2–√−v−1)2−ln(2–√+v+1)2

=−ln(2−(v+1)2)2+C (Where C is an arbitrary constant of indefinite integral