Math Question and Answers


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 107589 by mathdave last updated on 11/Aug/20

	Answered by Ar Brandon last updated on 11/Aug/20
	$I=∫(((x+6)/(x+8)))^6 dx=∫(1−(2/(x+8)))^6 dx =∫{1−((12)/(x+8))+((60)/((x+8)^2 ))−((160)/((x+8)^3 ))+((240)/((x+8)^4 ))−((192)/((x+8)^5 ))+((64)/((x+8)^6 ))}dx =x−12ln∣x+8∣−((60)/(x+8))+((80)/((x+8)^2 ))−((80)/((x+8)^3 ))+((48)/((x+8)^4 ))−((12,8)/((x+8)^5 ))+C$
	$I = \int {(\frac{x + 6}{x + 8})}^{6} dx = \int {(1 - \frac{2}{x + 8})}^{6} dx$ $= \int {1 - \frac{12}{x + 8} + \frac{60}{{(x + 8)}^{2}} - \frac{160}{{(x + 8)}^{3}} + \frac{240}{{(x + 8)}^{4}} - \frac{192}{{(x + 8)}^{5}} + \frac{64}{{(x + 8)}^{6}}} dx$ $= x - 12 \ln ∣ x + 8 ∣ - \frac{60}{x + 8} + \frac{80}{{(x + 8)}^{2}} - \frac{80}{{(x + 8)}^{3}} + \frac{48}{{(x + 8)}^{4}} - \frac{12, 8}{{(x + 8)}^{5}} + C$
	Answered by Her_Majesty last updated on 11/Aug/20

	$t = x + 8$ $\int \frac{{(t - 2)}^{6}}{t^{6}} d t =$ $= - 12 l n ∣ t ∣ + t - \frac{60}{t} + \frac{80}{t^{2}} - \frac{80}{t^{3}} + \frac{48}{t^{4}} - \frac{64}{5 t^{5}} =$ $= - 12 l n ∣ x + 8 ∣ - \frac{5 x^{6} + 240 x^{5} + 4500 x^{4} + 42000 x^{3} + 201200 x^{2} + 439280 x + 262976}{5 {(x + 8)}^{5}} + C$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum