A community for students.
Here's the question you clicked on:
 0 viewing
jonnymiller
 3 years ago
How do I find the indefinite integral of sin(x)/x ?
jonnymiller
 3 years ago
How do I find the indefinite integral of sin(x)/x ?

This Question is Closed

ahmedelmorsi
 3 years ago
Best ResponseYou've already chosen the best response.0its equal x*cos(x)cos(x)

guepardo14
 3 years ago
Best ResponseYou've already chosen the best response.0Integral [ (sin(x)/x) dx ] The fact of the matter is, this integral is one that cannot be expressed in terms of elementary functions. There's no way we can solve this using the methods we know; we cannot use integration by parts, partial fractions, substitution, trigonometric substitution, etc to solve this. We can, however, approximate the integral through a power series. sin(x) has its own power series, so all we need to do is divide each term of the series by x (this represents (1/x)sin(x), or sin(x)/x) and then integrate thereafter. como: Your proposed solution doesn't work, and here's why. Let 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.

ahmedelmorsi
 3 years ago
Best ResponseYou've already chosen the best response.0why we cant solve it by parts ???????????
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.