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Evaluate the integral: integral (4x2 + 4x + 4) dx

May 22, 2026Mathematics

ScanSolve AI Answer

Answer

\frac{4}{3}x^3 + 2x^2 + 4x + C

3 steps

Here's how to solve the integral:

Apply the sum rule for integrals.
$\int (4x^2 + 4x + 4) dx = \int 4x^2 dx + \int 4x dx + \int 4 dx$
Apply the constant multiple rule and the power rule for integration ( $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ ).
$= 4 \int x^2 dx + 4 \int x^1 dx + 4 \int x^0 dx$ $= 4 \left(\frac{x^{2+1}}{2+1}\right) + 4 \left(\frac{x^{1+1}}{1+1}\right) + 4 \left(\frac{x^{0+1}}{0+1}\right) + C$ $= 4 \left(\frac{x^3}{3}\right) + 4 \left(\frac{x^2}{2}\right) + 4 \left(\frac{x^1}{1}\right) + C$
Simplify the expression.
$= \frac{4}{3}x^3 + 2x^2 + 4x + C$
The final answer is $\frac{4}{3}x^3 + 2x^2 + 4x + C$ .