谢.不记得怎么解了.9/a'2+16/a'2-25=1

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谢.不记得怎么解了.9/a'2+16/a'2-25=1

两边乘a²(a²-25)
9a²-225+16a²=a四次方-25a²
a四次方-50a²+225=0
(a²-45)(a²-5)=0
a²=45,a²=5
这是椭圆吧
显然c²=25
因为a²>c²
所以a²=45

原式=1/2∫ln(x+1)dx²
=1/2x²ln(x+1)-1/2∫x²dln(x+1)
=[x²ln(x+1)]/2-1/2∫x²/(x+1)dx
单独求∫x²/(x+1)dx
=∫(x²-1+1)/(x+1)dx
=∫[(x²-1)/(x+1)+1/(x+1)]dx

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原式=1/2∫ln(x+1)dx²
=1/2x²ln(x+1)-1/2∫x²dln(x+1)
=[x²ln(x+1)]/2-1/2∫x²/(x+1)dx
单独求∫x²/(x+1)dx
=∫(x²-1+1)/(x+1)dx
=∫[(x²-1)/(x+1)+1/(x+1)]dx
=∫[(x-1)+1/(x+1)]dx
=∫(x-1)dx+∫dx/(x+1)
=x²/2-x+ln(x+1)+C
所以原式=[x²ln(x+1)]/2-x²/4+x/2-1/2*ln(x+1)+C
=[(x²-1)/2]ln(x+1)-x²/4+x/2+C

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