Math Problem Statement

Integrate 2x+x

Solution

To integrate the expression 2x+x2x + x, we first simplify it:

2x+x=3x2x + x = 3x

Now, the integral of 3x3x with respect to xx is:

3xdx=3x22+C\int 3x \, dx = \frac{3x^2}{2} + C

where CC is the constant of integration.

So, the result is:

3x22+C\frac{3x^2}{2} + C

Would you like a more detailed explanation of the steps, or do you have any further questions?

Here are some related questions for further exploration:

  1. What is the integral of x2x^2?
  2. How would you integrate 4x34x^3?
  3. What is the meaning of the constant of integration in indefinite integrals?
  4. How do you integrate a sum of terms like 3x+2x2+53x + 2x^2 + 5?
  5. Can you explain the power rule for integration?

Tip: When integrating polynomials, the power rule states that xndx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C, where n1n \neq -1.

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Math Problem Analysis

Mathematical Concepts

Algebra
Integral Calculus
Simplification of Expressions

Formulas

∫x^n dx = (x^(n+1))/(n+1) + C

Theorems

Power Rule for Integration

Suitable Grade Level

Grades 9-11