Question

Integrate :-

Answer 1

\[\int\limits \frac{ \sin x }{ x } dx\]

Answer 2

looks like you wrote it

Answer 3

isn't that the integral already?

Answer 4

Please Read the question carefully.

Answer 5

This is much easier if there are bounds on it, like from 0 to infinity.

Answer 6

Otherwise, you might just have to resort to integrating the power series. I don't think this one's a nice one.

Answer 7

This question is from indefinite integration.

Answer 8

GOOD LUCK! lol

Answer 9

As far as I know, this integral can't be done as written. You can approximate it by expanding sin(x) and then simplifying the expression, but it'll be an infinite series.

Answer 10

I think if it was easy, wolfram alpha wouldn't be giving it a special name.

http://www.wolframalpha.com/input/?i=integral%20sinx%2Fxdx&t=crmtb01

Answer 11

i thought the question said "write the integral" which is about what you can do

Answer 12

unless you want to expand \(\sin(x)\) in a power series, divide by \(x\) and then integrate term by term

Answer 13

please help me to solve this.

Answer 14

The question is to actually integrate it, it looks like. This can't be done exactly in closed form. The closest you can get is by writing sin(x) as:
\[\sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-...\]
Then simplify by dividing each term by x, then integrate. There will be a pattern, but there are an infinite number of terms, and no way to really simplify it.

Answer 15

didn't get it

Answer 16

what @Vandreigan is saying is that you are not going to get a nice closed form for this integral
some function \(F\) with \(F'(x)=\frac{\sin(x)}{x}\)

Answer 17

just because you write some integral, doesn't mean you can find it in a nice closed form

Answer 18

f(x) = (1/x)cos x - (1/x²)sinx + C

To make it easier to differentiate, factor (1/x).

f(x) = (1/x) [cos(x) - (1/x)sin(x)] + C

Differentiate using the product rule, noting that d/dx (1/x) = -1/x^2 gives us

f'(x) = (-1/x^2) [cos(x) - (1/x)sin(x)] + (1/x) [-sin(x) - [(-1/x^2)sin(x) + (1/x)cos(x)] ]

f'(x) = -cos(x)/x^2 + sin(x)/x^3 - sin(x)/x + sin(x)/x^2 - cos(x)/x

And as you can see, it looks nothing like sin(x)/x.