Use integration by parts to find the indefinite integral for each of the following functions involving a quotient.

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(a) (b) (x+7) 24.x dx Let f (x) = 24x and g'(x) = (x+7)4; then '(x) = 24 and g(x) = f(x+7)4 dx = }(x+7). Substituting, S 24.x (x+7)4 dx = = f(x) g(x) [ [g(x) '(x)] dx - = 24x [={}(x + 7)] / [ -={}(x + 7) 24] dx [6+3]-[ =-8x(x+7)-3 +8 +8(x+7) - dx Substituting 8 (x+7) dx = 4(x+7)2+c above, 24x (x+7)4 dx=-8x(x+7)-3-4(x+7) + c -8.x = - 4 (x+7)2+c (x+7)3 S- 22.x (x+4) dx Letting f(x)=-22x and g'(x) = (x+4), then f'(x) = -22 and g(x) = -2(x+4). Substituting in (12.6), | -22.x (x+4)3 dx = -22x [-10+4)-2]-[-10+4)-2-(2 (x =11x(x+4)-2. -/11 1(x+4)-2 dx dx Integrating again, -22.x (x+4)3 dx = 11x(x+4) + 11(x+4)+c