What Are the Correct u and du Values for These Trig Substitution Problems?

We can help you with understanding and correcting your work, but we cannot do your work for you. In summary, the conversation is about asking for help with trig substitution problems and receiving hints for solving them. The hints include finding a substitution for the first problem, using the property (am)n= amn for the second problem, and splitting the third problem into two integrals.
  • #1
qzack96
1
0
I really needed some help with these trig substitution problems. Please write the u and du values for each. I'd really really appreciate it !

1) Integrate [e^x/(e^x +1)] dx

2) Integrate [1/(e^2x +1)] dx

3) Integrate [(1+x)/(1+x^2)] dx

Thank you Again !
 
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  • #2
I will give you some hints.

d/dx (ex)=ex
d/dx(constant)=0

Can you think of a substitution for the first one?

(am)n= amn

what can you do with the second one now?

For the third, try making two integrals from it.
 
  • #3
qzack96 said:
Please write the u and du values for each.

Hi qzack96. I see that this is your first post. Welcome! When you post problems, especially homework problems, please try and show us what work you have done so far. It doesn't matter whether it is complete or correct. Post what you have tried or maybe what you try after following rock.freak667's hints.
 

FAQ: What Are the Correct u and du Values for These Trig Substitution Problems?

What is trig substitution and when is it used?

Trig substitution is a technique used in calculus to simplify integrals involving trigonometric functions. It is typically used when the integral involves a combination of algebraic and trigonometric functions.

How do I know when to use trig substitution?

Trig substitution is usually used when you have an integral with a combination of algebraic and trigonometric functions, and the trigonometric function can be rewritten in terms of a trigonometric identity.

What are the common trigonometric identities used in trig substitution?

The most commonly used trigonometric identities in trig substitution include sine and cosine identities such as sin^2(x) + cos^2(x) = 1 and the Pythagorean identities such as sin^2(x) = 1 - cos^2(x).

What are the three main types of trig substitution?

The three main types of trig substitution are:
1. Substitution with a sine function (x = a sin(t))
2. Substitution with a cosine function (x = a cos(t))
3. Substitution with a tangent function (x = a tan(t))

How do I solve integrals using trig substitution?

To solve integrals using trig substitution, you need to:
1. Identify which type of trig substitution to use
2. Substitute the appropriate trigonometric function
3. Simplify the integral using trigonometric identities
4. Solve the resulting integral
5. Substitute back to the original variable to get the final answer.

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