Question

$\int _ { 8 } ^ { 15 } \frac { d x } { ( x - 3 ) \sqrt { x + 1 } }$ equals

• A. log (5/3)
• B. log (3/5)
• C. 1/2 log (3/5)
• D. 1/2 log (5/3)

Answer 1

Answer: (D)

1/2 log (5/3)

Answer 2

Put x + 1 = t² ̃ dx = 2t dt

\ I = = 2 $\int _ { 3 } ^ { 4 } \frac { \mathrm { dt } } { \mathrm { t } ^ { 2 } - 4 }$ = 2. $\frac { 1 } { 2 ^ { 2 } } \left( \log \frac { t - 2 } { t + 2 } \right) _ { 3 } ^ { 4 }$

= $\frac { 1 } { 2 } \left[ \log \frac { 1 } { 3 } - \log \frac { 1 } { 5 } \right]$ = $\frac { 1 } { 2 } \log ( 5 / 3 )$