I'm solving some PDEs, and I'm stuck on the last step. The step before was to figure out $e_n$ given $f(x) = \sum_{n+0}^\infty e_n sin(n\pi x)$. I used the formula from the book $e_n = 2 \int_0^1 f(x) sin(n \pi x)$ and got a solution. For the last one my fourier series looks diffrent so I'm not sure how to proceed. It's $f(x) = \sum_{n+0}^\infty n \pi d_n sin(n\pi x)$. Up until now I never saw it with a factor $n \pi$ so I'm not sure what to do.
Would appriciate some help :)