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Question Number 215134 by RoseAli last updated on 29/Dec/24

Answered by Ghisom last updated on 29/Dec/24

∫(√(x−(√(x^2 −4))))dx= [t=(√(x−(√(x^2 −4)))) → dx=−((2(√(x^2 −4)))/t)dt] =∫(t^2 −(4/t^2 ))dt=(t^3 /3)+(4/t)= =((2(2x+(√(x^2 −4))))/3)(√(x−(√(x^2 −4))))+C

∫x−x2−4dx=[t=x−x2−4→dx=−2x2−4tdt]=∫(t2−4t2)dt=t33+4t==2(2x+x2−4)3x−x2−4+C

Answered by MrGaster last updated on 01/Jan/25

−2((1/2)(√(3−((√(x^2 −4)))^2 +4))+(3/2)ln∣(√(x^2 −4))+(√((3−(√(x^2 −4)^2 ))+4))∣+C)

−2(123−(x2−4)2+4+32ln∣x2−4+(3−x2−4)2+4∣+C)

Commented by Frix last updated on 01/Jan/25

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