Find the integral of sinx/x.

We can make use of taylor series of expansion.

Answer : The expression on integrating sin x / x is  x - (x³/3×3!) + (x⁵/5×5!) - (x⁷/7×7! ) + ....+ C

Let's look into the stepwise solution

Explanation:

Let us see the taylor series of expansion for sin x.

We have,

sin x = x - (x³/3!) + (x⁵/5!) - (x⁷/7!) + ..... upto infinite terms. [where ! sign denotes the factorial of a number]

sin x / x = 1/x { x - (x³/3!) + (x⁵/5!) - (x⁷/7!) + .....}

          =  1 - (x²/3!) + (x⁴/5!) - (x⁶/7!) + ....

Now,