Power series for § x²sin(x)dx

Question

johnweldon1993 · Answer

Find the power series for 

$$\large \int\limits^{}_{}x^{2}\sin(x)dx$$

amistre64 · Answer

whats the section symbol mean?  oh

sin(x) is fairly common

johnweldon1993 · Answer

yeah I dont know the integral alt key lol...

amistre64 · Answer

☺  alt 1 is about ill i recall of the alt combos

johnweldon1993 · Answer

and I believe that sin(x) = 

$$\large \sum_{}^{} \frac{(-1)^n x^{2n +1}}{(2n+1)}$$

Factorial on the bottom

amistre64 · Answer

assume sin(x) = sum f x^n

x^2 sin(x) = sum f x^(n+2)

integrating a polynomail ...   f x^(n+3)
                                          --------
                                              n+3

amistre64 · Answer

yeah, thats the sum of sin

amistre64 · Answer

missing a ! underndath, but close enough

johnweldon1993 · Answer

So hang on, just to be clear...since this is an integral, I cannot just make this x² times the sum of sin?

amistre64 · Answer

yeah

johnweldon1993 · Answer

Or do I actually have to integrate this by parts...

amistre64 · Answer

$$x^2(a_0+a_1x+a_2x^2+a_3x^3+...)=a_0x^2+a_1x^3a_2x^4+a_3x^5+...$$

amistre64 · Answer

lost a + inthere