\(\int_{-2}^{\alpha-1} \frac{1}{\left(1-2x-x^2\right)^{\frac{3}{2}}}\,\mathrm{d}x\quad \left(x+1=\sq

Question

$\int_{-2}^{\alpha-1} \frac{1}{\left(1-2x-x^2\right)^{\frac{3}{2}}}\,\mathrm{d}x\quad \left(x+1=\sqrt{2}\sin\theta,\ 0 < \alpha < 1\right)$

Accepted Answer

$ \frac{1}{2} \left(\frac{\alpha}{\sqrt{2-\alpha^2}} +1 \right)$ or $ \frac{1}{2} \left( \tan \left( \sin^{-1} \frac{\alpha}{\sqrt2} \right) +1 \right)$

HCI Integration Tutorial Q4 (g)

HCI Integration Tutorial Q4 (g)