Greetings! I'm not sure how to approach this question, it's asking that I rewrite this:
∫(sin(x)-x)/x^3 dx
as an infinite series. Any help is appreciated!
It might make more sense if you write it out as $\displaystyle sin(x)= x- x^3/3!+ x^5/5!- x^7/7!+ x^9/9!- \cdot\cdot\cdot$.
Then $\displaystyle sin(x)- x= - x^3/3!+ x^5/5!- x^7/7!+ x^9/9!- \cdot\cdot\cdot$
and $\displaystyle \frac{sin(x)- x}{x^3}= -1+ x^2/5!- x^4/7!+ x^6/9!- \cdot\cdot\cdot$
Integrate that.