A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Integrate xcos(5x)
so I set
g'(x) = x
f(x) = cos(5x)
Thus, I get
(x^(2)cos(5x)/2)  Integral of 5xcos(5x)
so I use substitution
u = 5x
du/5 = dx
therefore,
(x^(2)cos(5x)/2) + (1/5)integral of usin(u)
giving me
(x^(2)cos(5x)/2) + (5x^(2)cos(5x)/10) + c
what am I doing wrong the text book and wolfram alpha claims I have the wrong answer
anonymous
 4 years ago
Integrate xcos(5x) so I set g'(x) = x f(x) = cos(5x) Thus, I get (x^(2)cos(5x)/2)  Integral of 5xcos(5x) so I use substitution u = 5x du/5 = dx therefore, (x^(2)cos(5x)/2) + (1/5)integral of usin(u) giving me (x^(2)cos(5x)/2) + (5x^(2)cos(5x)/10) + c what am I doing wrong the text book and wolfram alpha claims I have the wrong answer

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0crud I just realized where I went wrong

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i mean antiderivative of a product

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0do I at least have the right idea with the substituion rule or am I way off?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0∫ x cos(5x) dx = integrate it by parts, assuming: x = u → dx = du cos(5x) dx = dv → (1/5) sin(5x) = v thus, recalling by parts integration rule, ∫ u dv = u v  ∫ v du, you get: ∫ x cos(5x) dx = (1/5)x sin(5x)  ∫ (1/5) sin(5x) dx = (1/5)x sin(5x)  (1/5) ∫ sin(5x) dx = (1/5)x sin(5x)  (1/5) [ (1/5)cos(5x)] + C = (1/5)x sin(5x) + (1/25) cos(5x) + C thus, in conclusion: ∫ x cos(5x) dx = (1/5)x sin(5x) + (1/25) cos(5x) + C I hope it helps.. Bye!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0man this migrane isn't helping me integrate integration by parts into my head
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.