Integrate the function x(2x+5)^0.5

integrate using substitution: (I = the symbol for integration)let u = 2x + 5 therefore x = (u - 5)/2 du/dx = 2 which means that du = 2dx ---> dx = 1/2 duThis means that the integral now = I((u - 5)/2 x u ^1/2 ) 1/2 du) = 1/4 I((u - 5) x 5u^1/2)du)when integrated this = (2/20 u^3/2 )- (10/12 u^3/2) + cthen substitute in u = 2x + 5 to get y = 1/10 (2x + 5)^5/2 - 5/6 (2x + 5)^3/2 + c