Questions: Question number 2. Find the indefinite integral ∫(2x^3+5x^2-3x+2)dx 1/2 x^4+5/3 x^3+3/2 x^2+2x+C 6x^2+C+10x-3 1/2 x^4+5/3 x^3-3x^2+2x+C 1/4 x^4+5/3 x^3-3/2 x^2+2x+C 1/2 x^4+5/3 x^3-3/2 x^2+2x+C

Question number 2.

Find the indefinite integral ∫(2x^3+5x^2-3x+2)dx
1/2 x^4+5/3 x^3+3/2 x^2+2x+C
6x^2+C+10x-3
1/2 x^4+5/3 x^3-3x^2+2x+C
1/4 x^4+5/3 x^3-3/2 x^2+2x+C
1/2 x^4+5/3 x^3-3/2 x^2+2x+C

Transcript text: Question number 2. Find the indefinite integral $\int\left(2 x^{3}+5 x^{2}-3 x+2\right) d x$ $\frac{1}{2} x^{4}+\frac{5}{3} x^{3}+\frac{3}{2} x^{2}+2 x+C$ $6 x^{2}+C+10 x-3$ $\frac{1}{2} x^{4}+\frac{5}{3} x^{3}-3 x^{2}+2 x+C$ $\frac{1}{4} x^{4}+\frac{5}{3} x^{3}-\frac{3}{2} x^{2}+2 x+C$ $\frac{1}{2} x^{4}+\frac{5}{3} x^{3}-\frac{3}{2} x^{2}+2 x+C$

Solution

Solution Steps

To find the indefinite integral of the polynomial $ \int (2x^3 + 5x^2 - 3x + 2) \, dx $, we will integrate each term separately. The power rule for integration states that the integral of $ x^n $ is $ \frac{x^{n+1}}{n+1} $. We apply this rule to each term of the polynomial and add a constant of integration $ C $.

Step 1: Define the Integral

We need to find the indefinite integral of the polynomial $ \int (2x^3 + 5x^2 - 3x + 2) \, dx $.

Step 2: Apply the Power Rule

Using the power rule for integration, we integrate each term separately: