indefinite integral

Question

x(4x+5)^8 dx

evaluate the indefinite integral

Answer 1

U = 4x+5

(1/4)(u-5)=x

Integrand is

(1/4)(u-5)u^8=

(1/4)[ u^9-5u^8]

Iintegrating

(1/4) [ (1/10)u^10- (5/9)u^9]

(1/40) u^10 - (5/36)u^9

U^9 [ (1/40) u -5/36]

(4x+5)^9[ (1/40)(4x+5)-5/36]

(4x+5) ^9[ x/10+1/8-5/36]

(4x+5)^9 [ x/10 - 1/72]