Question

Evaluate the integral ∫_0^1{36dx/((2x+1)^3)}

Answer 1

$36 \int\limits^1_0 { \frac{1}{(2 x + 1) ^{3} } } \, dx =$
u = 2 x + 1,  d u = 2 d x,  d x = d u / 2
$36*1/2 \int\limits^1_0 {u ^{-3} } \, du = 18 * t ^{-2}/(-2) = \\ - 9 * t^{-2}= \\ -9 * ( 2 x + 1 ) ^{-2}$
- 9 / ( 2 + 1 )² - ( - 9 / ( 0 + 1 )² = 
- 9 / 9 + 9 = - 1 + 9 = 8