Question

(1-x)^3/x integration

Answer 1

soln:

(a-b)³ = a³ + 3ab² - 3a²b - b³

use above formula:

(1 - x)³ = 1 + 3x² - 3x - x³

Now, (1-x)³/x = (1 + 3x² - 3x - x³)/x = 1/x + 3x - 3 - x² ----------(1)

integrate (1) both side

i.e, ∫(1-x)³/x dx = ∫(1/x + 3x - 3 - x²)dx = ∫1/x dx +3∫x dx - 3∫dx -∫x² dx
     
     ∫(1 - x)³/x dx = log(x) + 3/2x² - 3x - 1/3x³ +c


Hope it helps!