Homework Sourseuse the technique of substituting or integrtion by parts to
use the technique of substituting or integrtion by parts to evaluate the integrals ?3x(2x-1)^(3/2)
Solution
?3x(2x-1)^(3/2)dx u = 2x-1 du/dx = 2 du = 2dx dx = 1/2du x = (u+1)/2 xdx = ((u+1)/2)(1/2du) ?3/4(u+1)(u)^(3/2)du 3/4?(u+1)(u)^(3/2)du 3/4?(u^5/2+u^3/2)du 3/4 [?u^5/2 du + ?u^3/2 du] 3/4 [(2/7)u^(7/2) + (2/5)u^(5/2) ] by putting value of u 3/4 [(2/7)(2x-1)^(7/2) + (2/5)(2x-1)^(5/2) ] (6/28)(2x-1)^(7/2) + (6/20)(2x-1)^(5/2) (3/14)(2x-1)^(7/2) + (3/10)(2x-1)^(5/2)
