### Problem by finding an integral

I have to find the integral of ~~x~~*sqrt(x *`x*sqrt(x `

`+ 1) `~~dx.
~~dx

.

* **By hand, I found *~~(2/3)~~x*(x *`(2/3)*x*(x `

`+ 1)^(3/2) – `~~(4/15)~~

`(x (4/15)*(x + 1)^(5/2) + `~~c
~~c

.

By ~~sage math ~~SageMath I ~~found : -(2/3)~~*(x **found *`-(2/3)*(x `

`+ 1)^(3/2) + `~~(2/15)~~

`(x (2/15)*(x + `~~1)^(5/2) ~~1)^(5/2)

.

~~the sage math’s ~~ The SageMath code is simple:

~~x=var('x');
~~ ```
x = var('x')
f = x*sqrt(x +
```~~1);
~~1)
fi = integral(f, ~~x);
print (latex(fi));
which ~~x)
print(latex(fi))

Which is the ~~error? ~~error?