Question

\( \int_{0}^{T} \frac{1}{R-t V_{0}} \)

Answer 1

\(\int\limits^T_0 \frac{1}{r-tV_0}dt = \left[\frac{ln(R -tV_0)}{-V_0} \right]^T_0\)

\(= \frac{-ln(R- tV_0)}{V_0}+ \frac{lnR}{V_0}\)

\( = \frac{1}{V_0} ln\left(\frac{R}{R - tV_0}\right)\)