Math Problem Statement

∫ (2x + 3) dx

Solution

It looks like the image contains some mathematical notation. Let me analyze and extract the content to assist you with the solution.It seems that the text extraction did not yield any results. Let me manually review the image and interpret the mathematical expression.From the image, the problem appears to involve the integral of a function, specifically:

(2x+3)dx\int (2x + 3) \, dx

This is a straightforward integral problem. Let me solve it step by step:

Solution:

The integral of a polynomial function can be computed term by term. For this expression:

(2x+3)dx\int (2x + 3) \, dx

  1. Integrate each term:

    • The integral of 2x2x is 2x22=x2\frac{2x^2}{2} = x^2.
    • The integral of 33 is 3x3x.
  2. Combine the results: x2+3x+Cx^2 + 3x + C

Where CC is the constant of integration.

Final Answer:

x2+3x+Cx^2 + 3x + C

Would you like more details or have any questions on this?

Here are some related questions to explore further:

  1. How do you handle integrals with more complex polynomials?
  2. What happens when you integrate a constant term?
  3. Can integration be applied to trigonometric functions?
  4. How do you compute definite integrals as opposed to indefinite ones?
  5. What are some practical applications of integration in physics or engineering?

Tip: When solving indefinite integrals, always remember to add the constant of integration CC, as indefinite integrals represent a family of functions.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Integral Calculus
Polynomial Integration

Formulas

∫ ax^n dx = (a/(n+1))x^(n+1) + C
∫ c dx = cx + C

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12