## 400 Reputation

16 years, 242 days

## thanks. here \$n\$ is a...

thanks.

here \$n\$ is a positive number n >= 1.

i am interested in finding a closed form for the integral. is it possible:

## thanks. here \$n\$ is a...

thanks.

here \$n\$ is a positive number n >= 1.

i am interested in finding a closed form for the integral. is it possible:

## Thanks. I want a formula...

Thanks. I want a formula that works for all n

But when i do

> `> `assuming`([diff(1/(1+x^2), `\$`(x, n))], [n::posint]);

maple gives
/  1            \
diff|------, [x \$ n]|
|     2         |
\1 + x          /

maple does not give

(n!/2)*(-exp(-(1/2)*n*ln(1+x^2))*sin(n*arctan(1, -x))*x+exp(-(1/2)*n*ln(1+x^2))*cos(n*arctan(1, -x))+exp(-(1/2)*n*ln(1+x^2))*sin(n*arctan(-1, -x))*x+exp(-(1/2)*n*ln(1+x^2))*cos(n*arctan(-1, -x)))/(1+x^2)

## Thanks. I want a formula...

Thanks. I want a formula that works for all n

But when i do

> `> `assuming`([diff(1/(1+x^2), `\$`(x, n))], [n::posint]);

maple gives
/  1            \
diff|------, [x \$ n]|
|     2         |
\1 + x          /

maple does not give

(n!/2)*(-exp(-(1/2)*n*ln(1+x^2))*sin(n*arctan(1, -x))*x+exp(-(1/2)*n*ln(1+x^2))*cos(n*arctan(1, -x))+exp(-(1/2)*n*ln(1+x^2))*sin(n*arctan(-1, -x))*x+exp(-(1/2)*n*ln(1+x^2))*cos(n*arctan(-1, -x)))/(1+x^2)

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