Integrate 6x2 - x + 3 with respect to x.

Question

ScanSolve AI Tutor · Accepted Answer

let's integrate this expression.

The problem asks to evaluate the indefinite integral:

\int (6x^2 - x + 3) \,dx

Apply the linearity property of integration, which states that the integral of a sum or difference is the sum or difference of the integrals.
$\int 6x^2 \,dx - \int x \,dx + \int 3 \,dx$
Integrate each term using the power rule for integration, $\int x^n \,dx = \frac{x^{n+1}}{n+1} + C$ , and the rule for integrating a constant, $\int k \,dx = kx + C$ .
For the first term, $\int 6x^2 \,dx$ :
$6 \cdot \frac{x^{2+1}}{2+1} = 6 \cdot \frac{x^3}{3} = 2x^3$
For the second term, $\int x \,dx$ (which is $\int x^1 \,dx$ ):
$\frac{x^{1+1}}{1+1} = \frac{x^2}{2}$
For the third term, $\int 3 \,dx$ :
$3x$
Combine the results of each integral and add the constant of integration, $C$ , since it's an indefinite integral.
$2x^3 - \frac{x^2}{2} + 3x + C$

Answer