Question
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Find the trigonometric integral. (Use for the constant of integration.)

Ask by Little Reid. in the United States
Mar 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The integral of with respect to is .

Solution

Calculate the integral .
Evaluate the integral by following steps:
  • step0: Evaluate using formulas and rules:
  • step1: Evaluate the integral:
  • step2: Simplify the expression:
  • step3: Add the constant of integral C:

    The trigonometric integral of is , where is the constant of integration.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Bonus Knowledge

To solve the integral , we can use integration by substitution.
Let . Then, the derivative of is:
Since and , we can rewrite our integral as follows:
This integral can be a bit complicated but an alternative way is to integrate by using the identity and separate out parts of the integral:
Now let’s integrate by parts. Let and . This gives us:
The integration steps involve some manipulation which results in:
So the final result is:
Thus, the integral evaluates to:

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