# Two ways of integrating x↦xⁿsin(x) give contradictory results. Bug?

**First way:**

```
var('x,n')
integral(x^n*sin(x),x)
```

gives just

```
integrate(x^n*sin(x), x)
```

not very informative, let us try to add an assumption to get nicer results.

**Second way:**

```
assume(n,'integer')
integral(x^n*sin(x),x)
```

gives

```
1/4*(((-1)^n - 1)*gamma(n + 1, I*x) - ((-1)^n - 1)*gamma(n + 1, -I*x))*(-1)^(-1/2*n)
```

Uhm, looks better, but... wait, isn't `(-1)^n-1`

equal to `0`

for even values of `n`

? That would make the whole thing equal to `0`

for even `n`

.

```
I = integral(x^n*sin(x),x)
for k in range(10):
print I.subs(n==2*k)
```

prints only `0`

s. Weird, non-zero functions should not have zero integrals.

**Third way :**

Let us try to do the integration with particular values of `n`

.

```
for n in range(5):
print integral(x^n*sin(x),x)
```

prints

```
-cos(x)
-x*cos(x) + sin(x)
-(x^2 - 2)*cos(x) + 2*x*sin(x)
-(x^3 - 6*x)*cos(x) + 3*(x^2 - 2)*sin(x)
```

Looks better, but is clearly different from the previous answer.

**Question:**

I am working on the cloud, with SageMath 7.4 kernel. Is this a bug or did I misunderstood the meaning of the `'integer'`

assumption ?

If this is a bug, how should I report it, is posting this question here enough ?

P.S. I did read the wiki page about reporting bugs, but, gosh, is it really necessary to have a google account in order to report a bug ? Both sage-devel and sage-support are on Google Groups.