How to Integrate Complex Functions Like ∫(sec(x^2))(e^cot(x))dx?

  • Thread starter dasboot58
  • Start date
In summary, the conversation is about someone seeking help with two integration problems. They are asked to post their attempt at the problem, but they are unable to do so and ask for help. The conversation is eventually closed by the moderator due to violation of forum rules.
  • #1
dasboot58
6
0
<< Moderator's Note -- Original post (OP) restored after being deleted by the poster >> PLEASE HELP! Does anyone possible know how to do these two problems! I'm freaking out!

∫(secx^2)(e^cotx)dx

Thank you so much!

PLEASE HELP! Does anyone possible know how to do these two problems! I'm freaking out!

∫(secx^2)(e^cotx)dx

And∫9x^3/Square root of (1+x^2) dx NEED TO USE SUBSTITUTION X=TanxThank you so much!
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Urgent!

These seem like homework problems...
Please post an attempt at the problem, and this should be in the homework section,
Cheers,
 
  • #3
No these are review questions I'm stuck on. All my answers are wrong. Everything doesn't make sense but apparently there is an answer to this.
 
  • #4
Urgent!

When I get home I will attempt to solve them. Could you post yours steps so that we can see where you may have gone wrong?

See the FAQ for how to use latex.
 
  • #5
Is there a model forum? I can take a picture with my phone. I have about 20 different approaches all leading to THE WRONG ANSWER! When I graph it comes close but not it. I asked my old math professor and he doesn't know. Think he should get fired but that's a different story.
 
  • #6
Post what you think is your best attempt.
 
  • #7
I figured this one out! Can you help me with the other?
 
Last edited:
  • #8
dasboot58 said:
I figured this one out! Can you help me with the other?

I only saw one problem, I can't see your other one. I can't see your work, this is the wrong location. Also, naming a posting urgent is a bad way to get help here.

As far as the one I can see. Are we assuming x is real? Do you know about exponential integrals?
 
  • #9
Student100 said:
I only saw one problem, I can't see your other one. I can't see your work, this is the wrong location. Also, naming a posting urgent is a bad way to get help here.

As far as the one I can see. Are we assuming x is real? Do you know about exponential integrals?

I edited the post. I do have a basic knowledge. I've done a lot of problems similar to this. With this one, I honestly have no idea how to begin..
 
  • #10
dasboot58 said:
I edited the post. I do have a basic knowledge. I've done a lot of problems similar to this. With this one, I honestly have no idea how to begin..

Are you trying to do it by parts? What is your u and v?
 
  • #11
Student100 said:
Are you trying to do it by parts? What is your u and v?

I don't think you can do it by parts. I'm guessing U would be secx^2 and ∫dv=∫e^cotx
 
  • #12
Thread closed temporarily for Moderation...
 
  • #13
Thread will stay closed.

@dasboot58 -- Check your PMs. You've broken at least a half-dozen of the PF rules with this thread.

For everybody else, please report threads where the OP shows no work. Thank you.
 

Related to How to Integrate Complex Functions Like ∫(sec(x^2))(e^cot(x))dx?

What is the first step in solving the integral?

The first step in solving this integral is to recognize that it is a trigonometric integral and use a trigonometric substitution. In this case, we can substitute u = cotx and du = -csc^2xdx.

How do we handle the secant squared term in the integral?

Since we have substituted for cotx, we can use the identity sec^2x = 1 + cot^2x to rewrite the integral as ∫(1 + u^2)(e^-u)du.

What is the next step after rewriting the integral?

After rewriting the integral, we can use the power rule for integration to solve for each term separately. In this case, the first term can be integrated using the rule ∫e^x = e^x + C, and the second term can be integrated using the rule ∫u^n = u^(n+1)/(n+1) + C.

Is there anything else we need to consider when solving this integral?

Yes, we also need to consider the limits of integration. Since we used a substitution, we need to convert the original limits in terms of x to limits in terms of u. We can do this by plugging in the original limits into our substitution equation u = cotx.

What is the final solution to the integral?

After integrating each term and converting the limits of integration, we can simplify to get the final solution of ∫(secx^2)(e^cotx)dx = e^cotx + (1/3)cot^3x + C, where C is the constant of integration.

Similar threads

I Integration of ##e^{-x^2}## with respect to ##x##
    • Calculus
Replies
4
Views
1K
I How Do You Integrate 1/√(x^3 + x^2 + x + 1) dx?
    • Calculus
Replies
8
Views
1K
B Integrating sec(x): Understanding the Answer
    • Calculus
Replies
6
Views
2K
MHB Solve Complex Integration: Find 2.36 Area of y=-x/2e+1/e+e & y=e^x/2
    • Calculus
Replies
10
Views
1K
Integrals that keep me up at night
    • Calculus and Beyond Homework Help
Replies
22
Views
1K
MHB If y=sin5 + log base 10 x+ 2 sec x find dy/dx
    • Calculus
Replies
7
Views
1K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
    • Calculus and Beyond Homework Help
Replies
7
Views
742
I Prove Complex Integral: $\int_m^\infty\sqrt{x^2-m^2}e^{-ixt}dx$
    • Calculus
Replies
1
Views
1K
MHB Integral of sec(x): Solving with Substitution
    • Calculus
Replies
4
Views
2K
MHB How to Solve the Integral Problem ∫(tan3x/sec2x)dx?
    • Calculus
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top