A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
I really need help with this trig substitution please.
integral of (x^3)/sqrt(9(x^2)+49)
 2 years ago
I really need help with this trig substitution please. integral of (x^3)/sqrt(9(x^2)+49)

This Question is Closed

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1You have to do two different substitutions... First, set u=x², so du=2xdx. The integral becomes:\[\int\limits_{}^{}\frac{ udu }{ \sqrt{9u+49 }}\]Next, set p = 9u+49, so dp=9du, giving:\[\frac{ 1 }{ 81 } \int\limits_{}^{}\frac{ p49 }{ \sqrt{p} }dp\]Now you can split up the fraction:\[\frac{ 1 }{ 81 }\int\limits_{}^{}\left( p^{\frac{1}{2}}49p^{\frac{1}{2}} \right)dp\]This is not difficult anymore, I guess...

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1Oops, forgot to compensate with ½ for the 2x, so replace 1/81 by 1/162, to get even!

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1If that second step is a little hard to follow, then here's extra explanation: p=9u+49, so u= (p49)/9 = 1/9 *(p49). Also: dp=9du, so du = 1/9 * dp. That accounts for the 1/81. Extra factor 1/2 I forgot, gives you 1/162.

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1@MajikDUSTY: I think it's your turn now ;)

Hoa
 2 years ago
Best ResponseYou've already chosen the best response.0perfect way and new to me. thanks for that

Hoa
 2 years ago
Best ResponseYou've already chosen the best response.0Question: do we have to be back to u and then to x to get the final answer or just stop at p, since we substitute and respect to u and then to p dp ? just a little bit confuse

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1No, you have to go back to x. First go from p to u, then from u to x, so in the end you'll have a nice (ahem) formula with x...

Hoa
 2 years ago
Best ResponseYou've already chosen the best response.0got it. I'm not asker. I read it and recognize that the way you solve the problem is really new to me. Just confirm the stuff. Thanks a lot

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1You're right. Glad to be of help.
Ask your own question
Ask a QuestionFind 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.