Language and more detailed

edited Sep 24, 2015 at 14:32

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I have a integral, but and I use two different symbols in an interchangeable way, but canI do not get same expressions when I swap them. Can some one explain why?

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y}, Assumptions -> 0 < y < x]

Log[(x + y + 2 Sqrt[x y])/(x - y)]

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x}, Assumptions -> 0 < x < y]

2 ArcTanh[Sqrt[x/y]]

I have a integral, but I use two different symbols, but can not get same expressions. Can some one explain why?

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y}, Assumptions -> 0 < y < x]

Log[(x + y + 2 Sqrt[x y])/(x - y)]

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x}, Assumptions -> 0 < x < y]

2 ArcTanh[Sqrt[x/y]]

I have a integral and I use two different symbols in an interchangeable way, but I do not get same expressions when I swap them. Can some one explain why?

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y}, Assumptions -> 0 < y < x]

Log[(x + y + 2 Sqrt[x y])/(x - y)]

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x}, Assumptions -> 0 < x < y]

2 ArcTanh[Sqrt[x/y]]

Routine clean-up

Source Link

edited Sep 24, 2015 at 14:29

m_goldberg

108.6k
16
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Can someone explain why mathematica is so "silly"? Evaluating two equivalent integrals apparently gives two different results

I have a integral, but I use two different symbols, but can not get same expressions. Can some one explain why?[![enter image description here][1]]

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y},  Assumptions -> 0 < y < x] (*Out= Log[(x + y + 2 Sqrt[x y])/(x - y)]*)

Log[(x + y + 2 Sqrt[x y])/(x - y)]

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x},  Assumptions -> 0 < x < y] (*Out= 2 ArcTanh[Sqrt[x/y]]*)

2 ArcTanh[Sqrt[x/y]]

Can someone explain why mathematica is so "silly"?

I have a integral, but I use two different symbols, but can not get same expressions. Can some one explain why?[![enter image description here][1]]

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y},  Assumptions -> 0 < y < x] (*Out= Log[(x + y + 2 Sqrt[x y])/(x - y)]*)  Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x},  Assumptions -> 0 < x < y] (*Out= 2 ArcTanh[Sqrt[x/y]]*)

Evaluating two equivalent integrals apparently gives two different results

I have a integral, but I use two different symbols, but can not get same expressions. Can some one explain why?

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y}, Assumptions -> 0 < y < x]

Log[(x + y + 2 Sqrt[x y])/(x - y)]

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x}, Assumptions -> 0 < x < y]

2 ArcTanh[Sqrt[x/y]]

Provide the mathematica expressions

Source Link

edited Sep 24, 2015 at 14:18

yohbs

7.1k
3
30
61

I have a integral, but I use two different symbols, but can not get same expressions. Can some one explain why?[![enter image description here][1]]

In[326]:= Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y}, Assumptions -> 0 < y < x] Out[326]=(*Out= Log[(x + y + 2 Sqrt[x y])/(x - y)]]*) In[328]:= Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x}, Assumptions -> 0 < x < y] Out[328]=(*Out= 2 ArcTanh[Sqrt[x/y]]y]]*)

I have a integral, but I use two different symbols, but can not get same expressions. Can some one explain why?

In[326]:= Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y}, Assumptions -> 0 < y < x] Out[326]= Log[(x + y + 2 Sqrt[x y])/(x - y)] In[328]:= Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x}, Assumptions -> 0 < x < y] Out[328]= 2 ArcTanh[Sqrt[x/y]]

I have a integral, but I use two different symbols, but can not get same expressions. Can some one explain why?[![enter image description here][1]]

Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, y}, Assumptions -> 0 < y < x] (*Out= Log[(x + y + 2 Sqrt[x y])/(x - y)]*) Integrate[1/Sqrt[(x - t) (y - t)], {t, 0, x}, Assumptions -> 0 < x < y] (*Out= 2 ArcTanh[Sqrt[x/y]]*)