integral dari x-9/akar x-3 dx adalah

[tex]f(x)dx \\ f( \frac{x - 9}{ \sqrt{x - 3} } )dx \\ \\ = \frac{ \frac{1}{2} {x}^{2} - 9x }{ \frac{ ({x - 3})^{ \frac{3}{ 2} } }{ \frac{3}{2} } } \\ \\ = \frac{ 3 \times (\frac{1}{2} {x}^{2} - 9x)}{2 \times ( { x - 3})^{ \frac{3}{2} } } \\ \\ = \frac{3( \frac{1}{2} {x}^{2} - 9) }{2 \sqrt[2]{( x - 3) ^{3} } } \\ \\ = \frac{3( \frac{1}{2} {x}^{2} - 9)}{2(x - 3) \sqrt{x - 3} } \\ \\ = \frac{3( \frac{1}{2} {x}^{2} - 9) \times (x + 3)}{2(x - 3)(x - 3 )} \times \frac{2}{2} \\ \\ = \frac{(3 {x}^{2} - 54)(x + 3)}{4(x - 3)^{2} } \\ \\ = \frac{3 {x}^{3} + 9 {x}^{2} - 54x - 162 }{4 {x}^{2} - 24x + 36}[/tex]