Evaluate the indefinite integral as an infinite series
Integral of (sinx/4x) and find the first 5 non-zero
terms

I know that you are suppose to do sinx=x-x^3/3!+x^5/5!-x^7/7!+x^9/9!

then divide it by 4x then integrate each term and I get sinx/4x=1/4-x^2/(4*3!)+x^4/( 4*5!)-x^6/(4*7!) etc..
then you integrate and you get x/4-x-x^3/(4*3!*3)+x^5/(4*5*5!)-x^7/(4*7* 7!) etc

when I enter this in it is not right! am I doing something wrong?

Question

Evaluate the indefinite integral as an infinite series
Integral of (sinx/4x) and find the first 5 non-zero 
terms

I know that you are suppose to do sinx=x-x^3/3!+x^5/5!-x^7/7!+x^9/9! 

then divide it by 4x then integrate each term and I get sinx/4x=1/4-x^2/(4*3!)+x^4/( 4*5!)-x^6/(4*7!) etc..
then you integrate and you get x/4-x-x^3/(4*3!*3)+x^5/(4*5*5!)-x^7/(4*7* 7!) etc

when I enter this in it is not right! am I doing something wrong?