Here is the function which could easily be solved using expansion method but how could I solve it using integration by parts
$$\int y^4(1-y)^3 dy$$
The problem is, when I apply integration by parts to solve it, it is never ending solution and I am not able to get the answer.
For example, I let $u = (1-y)^3$ and $dv = (y^4)$, so $du = 3(1-y)^2$ and $v = \dfrac{y^5}{5}$
When I apply the Integration by Parts formula,
$$uv - \int v du$$
I got the kind of same equation as I started with, so I need to apply integration by parts once again, and then again. How many times is it required to apply before I get the answer ?