Math Problem Statement
Solution
The integral in the image is:
Let's solve it step-by-step.
Step 1: Factor Out the Constant
Since is a constant multiplier, we can take it out of the integral:
Step 2: Split the Integral
We can split the integral into two separate integrals:
Step 3: Integrate Each Term
-
Integrate :
-
Integrate :
Using the formula , we get:
Step 4: Combine Results
Now, substitute back into the integral:
Step 5: Simplify
Distribute the :
Final Answer
where is the constant of integration.
Would you like further clarification on any part of this solution, or details on trigonometric integrals?
Here are some related questions you might find useful:
- How do we handle integrals with trigonometric functions in general?
- What is the formula for integrating a constant multiplied by a trigonometric function?
- How does the constant factor impact the integration process?
- What other common methods are there for integrating functions like these?
- How do you verify an indefinite integral solution?
Tip: Always remember to include the constant of integration when solving indefinite integrals.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Integration
Trigonometric Functions
Constant Multipliers
Formulas
∫ sin(ax) dx = - (1/a) cos(ax)
Constant multiple rule: ∫ c*f(x) dx = c * ∫ f(x) dx
Theorems
-
Suitable Grade Level
Grades 11-12 or introductory college-level calculus
Related Recommendation
Integration of t^7 sin(2t^4): A Substitution Method Example
Evaluate the Integral ∫ sin(6x - 2) dx Using Substitution
Integral of (7 sin(x) + 4 sec(x)) / tan(x) Step-by-Step Solution
Solve the Integral \( \int \frac{dt}{(1 - 6t)^4} \) using Substitution
Integration of \( \int \tan(6x) \, dx \) – Step-by-Step Solution