## 1481 Reputation

8 years, 192 days

## Cross post in Mathematics site....

Cross post. in Mathematics site.

## @Sayed  Looks like fourier ca...

Looks like fourier can't solve for: "sech(x)^3" and "tanh(x)*sech(x)^3".

## Using comparision test from this video, ...

Using comparision test from this video, we have:

```0 <= (x + 2)/((2*x^3 + 1)*ln(x)) and (x + 2)/((2*x^3 + 1)*ln(x)) <= 1/ln(x)

int(1/ln(x), x = 1 .. infinity);

#infinity

```

## Numerically....

It can be done only numerically.

```a := 0;
b := 1;
int(exp(-1/sqrt(x^2 + 1)), x = a .. b, numeric);

#0.4160094117```

## @Viva I don't have any  su...

I don't have any  suggestions ,because Maple can't solve solvelable integrals.

Maple is weak for solving  indefinite and define integrals.

2_ver2.mw

## Can't....

Mathematica 13.0 also can't integrate.

Better post this question to this webpage.

## Try:...

int(A,theta=0..eta)

## @C_R  The problem in Maple is:&nbs...

The problem in Maple is: '"automatic simplification' and 'evaluation'".

See here , here and here.

## duplicates and close followups...

Cross post here. and here

1.What you need PDEtools for that?

2.You want to solve a Nonlinear Volterra Integro Differential Equation ?, if yes post the equation.

## To close....

I'm voting to close this question as off-topic because there is no well-posed question in this post; the OP is simply asking for somebody to act as a free coding service.

## To close....

I'm voting to close this question as off-topic because there is no well-posed question in this post; the OP is simply asking for somebody to act as a free coding service.

## This line of code dosen't work: su...

This line of code dosen't work:

`sum(sum((k[1]+3)!*((-1)^(k-k[1]-1)/2)*Y[k[1]+3]/(k[1]!*(k-k[1])!,k[1]=0..k)`

?

## No reference....

I don't have reference.

I'm played with this sum a few minutes and I found  generalization.

## Generalization:...

```restart;

n := 2;

Sum(Beta(k, c)/(a*k + b)^n, k = 1 .. infinity) = GAMMA(c)*hypergeom([1, 1, seq(1 + b/a, j = 1 .. n)], [seq(2 + b/a, j = 1 .. n), 1 + c], 1)/(GAMMA(1 + c)*(a + b)^n);```

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