Definitely solved Indefinite Integral!

Here is the solution

$\large\ \int { \frac { x }{ \left( 5 - 4x - { x }^{ 2 } \right) } dx } = \int { \frac { x }{ \left( 9 - { \left( x + 2 \right) }^{ 2 } \right) } dx }$ .

Now substitute

$\left( x + 2 \right) = 3\sin { \theta }$ , to get

$\large\ \begin{aligned} \int { \frac { x }{ \left( 5 - 4x - { x }^{ 2 } \right) } dx } = \int { \frac { x }{ \left( 9 - { \left( x + 2 \right) }^{ 2 } \right) } dx } = \int { \frac { \left( 3\sin { \theta } - 2 \right) }{ { \left( 3\cos { \theta } \right) }^{ 2 } } d\theta } = \int { \frac { \tan { \theta } \sec { \theta } }{ 3 } d\theta } - \int { \frac { 2 }{ 9 } \sec ^{ 2 }{ \theta } d\theta } = \frac { \sec { \theta } }{ 3 } - \frac { 2 }{ 9 } \tan { \theta } + C \end{aligned}$ .