Evaluate the integral of (5x^3 - 3x + 2) dx.

Evaluate the integral of (5x^3 - 3x + 2) dx.

• A. (5/4)x^4 - (3/2)x^2 + 2x + C
• B. (5/4)x^4 - (1/2)x^2 + 2x + C
• C. (4/5)x^4 - (1/2)x^2 + x + C
• D. (5/4)x^4 - 3x + 2 + C

Answer: (A)

To evaluate the integral of the expression \(5x^3 - 3x + 2\), we apply basic integration rules. The integral of a power function \(x^n\) is given by \(\frac{x^{n+1}}{n+1}\), plus the constant of integration \(C\). 1. For the term \(5x^3\), applying the integral formula: \[ \int 5x^3 \, dx = 5 \cdot \frac{x^{3+1}}{3+1} = 5 \cdot \frac{x^4}{4} = \frac{5}{4}x^4. \] 2. For the term \(-3x\), we have: \[ \int -3x \, dx = -3 \cdot \frac{x^{1+1}}{1+1} = -3 \cdot \frac{x^2}{2} = -\frac{3}{2}x^2. \] 3. Finally, for the constant term \(2\): \[ \int 2 \, dx = 2x. \

To evaluate the integral of the expression (5x^3 - 3x + 2), we apply basic integration rules. The integral of a power function (x^n) is given by (\frac{x^{n+1}}{n+1}), plus the constant of integration (C).

1. For the term (5x^3), applying the integral formula:

[

\int 5x^3 , dx = 5 \cdot \frac{x^{3+1}}{3+1} = 5 \cdot \frac{x^4}{4} = \frac{5}{4}x^4.

]

2. For the term (-3x), we have:

[

\int -3x , dx = -3 \cdot \frac{x^{1+1}}{1+1} = -3 \cdot \frac{x^2}{2} = -\frac{3}{2}x^2.

]

3. Finally, for the constant term (2):

[

\int 2 , dx = 2x.

\