Mixing
Show $int_{0}^{-x}frac{t^n}{1-t}dt=(-1)^{n+1}int_{0}^{x}frac{t^n}{1+t}dt$ for $-1<x<1$.
$begingroup$
Show $int_{0}^{-x}frac{t^n}{1-t}dt=(-1)^{n+1}int_{0}^{x}frac{t^n}{1+t}dt$ for $-1<x<1$.
Maybe I'm not thinking straight today but I can't seem to justify the above.
calculus
asked Jan 31 at 1:48
helios321helios321
56849
$endgroup$
add a comment |
$begingroup$
Show $int_{0}^{-x}frac{t^n}{1-t}dt=(-1)^{n+1}int_{0}^{x}frac{t^n}{1+t}dt$ for $-1<x<1$.
Maybe I'm not thinking straight today but I can't seem to justify the above.
calculus
asked Jan 31 at 1:48
helios321helios321
56849
$endgroup$
$begingroup$
Seems that expansion into power series could do it.
$endgroup$
– xbh
Jan 31 at 1:50
add a comment |
$begingroup$
Show $int_{0}^{-x}frac{t^n}{1-t}dt=(-1)^{n+1}int_{0}^{x}frac{t^n}{1+t}dt$ for $-1<x<1$.
Maybe I'm not thinking straight today but I can't seem to justify the above.
calculus
asked Jan 31 at 1:48
helios321helios321
56849
$endgroup$
Show $int_{0}^{-x}frac{t^n}{1-t}dt=(-1)^{n+1}int_{0}^{x}frac{t^n}{1+t}dt$ for $-1<x<1$.
Maybe I'm not thinking straight today but I can't seem to justify the above.
calculus
calculus
asked Jan 31 at 1:48
helios321helios321
56849
asked Jan 31 at 1:48
helios321helios321
56849
asked Jan 31 at 1:48
helios321helios321
56849
asked Jan 31 at 1:48
helios321helios321
56849
asked Jan 31 at 1:48
helios321helios321
56849
56849
$begingroup$
Seems that expansion into power series could do it.
$endgroup$
– xbh
Jan 31 at 1:50
add a comment |
$begingroup$
Seems that expansion into power series could do it.
$endgroup$
– xbh
Jan 31 at 1:50
$begingroup$
Seems that expansion into power series could do it.
$endgroup$
– xbh
Jan 31 at 1:50
$begingroup$
Seems that expansion into power series could do it.
$endgroup$
– xbh
Jan 31 at 1:50
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint: use the change of variable $t = -u$.
answered Jan 31 at 1:54
Diego Cornejo KocDiego Cornejo Koc
314
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Hint: use the change of variable $t = -u$.
answered Jan 31 at 1:54
Diego Cornejo KocDiego Cornejo Koc
314
$endgroup$
add a comment |
$begingroup$
Hint: use the change of variable $t = -u$.
answered Jan 31 at 1:54
Diego Cornejo KocDiego Cornejo Koc
314
$endgroup$
add a comment |
$begingroup$
Hint: use the change of variable $t = -u$.
answered Jan 31 at 1:54
Diego Cornejo KocDiego Cornejo Koc
314
$endgroup$
Hint: use the change of variable $t = -u$.
answered Jan 31 at 1:54
Diego Cornejo KocDiego Cornejo Koc
314
answered Jan 31 at 1:54
Diego Cornejo KocDiego Cornejo Koc
314
answered Jan 31 at 1:54
Diego Cornejo KocDiego Cornejo Koc
314
answered Jan 31 at 1:54
Diego Cornejo KocDiego Cornejo Koc
314
314
add a comment |
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$begingroup$
Seems that expansion into power series could do it.
$endgroup$
– xbh
Jan 31 at 1:50