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Question Number 84123 by Roland Mbunwe last updated on 09/Mar/20

∫((5−x)/(1+(√((x−4)))))

∫5−x1+(x−4)

Commented by mathmax by abdo last updated on 09/Mar/20

I=∫ ((5−x)/(1+(√(x−4))))dx we do the changement (√(x−4))=t ⇒x−4=t^2 I =∫ ((5−(4+t^2 ))/(1+t)) (2t)dt =2 ∫ ((t(1−t^2 ))/(1+t))dt =2∫ ((t(1−t)(1+t))/(1+t))dt =2∫ (t−t^2 )dt =2((t^2 /2)−(t^3 /3))+C =t^2 −(2/3)t^3 +C =x−4 −(2/3)(x−4)^(3/2) +C

I=∫5−x1+x−4dxwedothechangementx−4=t⇒x−4=t2I=∫5−(4+t2)1+t(2t)dt=2∫t(1−t2)1+tdt=2∫t(1−t)(1+t)1+tdt=2∫(t−t2)dt=2(t22−t33)+C=t2−23t3+C=x−4−23(x−4)32+C

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