Question

use u-substituion rule to find the anti derivative of
(x/9-1)^1/2 dx

Answer 1

\[\int\limits_{}^{} (\frac {x}{9} - 1)^{\frac {1}{2}}dx\]\[u = \frac {x}{9} - 1, 9du = dx\]\[9 \int\limits\limits\limits_{}^{} u^{\frac {1}{2}}du = 9 * \frac {2}{3} u^{ \frac {3}{2}} + C = 6 u^{ \frac{3}{2}} + \]\[\int\limits\limits_{}^{} (\frac {x}{9} - 1)^{\frac {1}{2}}dx = 6 (\frac {x}{9} - 1)^{\frac{3}{2}} + C\]

Answer 2

u^2 = (x/9) -1 --> 2udu = (1/9)dx => dx = 18udu
= 18 Int (udu) = 9 u^2 = 9 sqrt [( x/9 -1)] + C