find ∫(12x + 7)dx. ∫(12x + 7)dx = □

Explanation:

Step1: Apply sum - rule of integration

$\int(12x + 7)dx=\int12x dx+\int7dx$

Step2: Integrate $\int12x dx$

Using the power - rule $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$), for $\int12x dx$, since $\int12x dx=12\int x dx$, and $\int x dx=\frac{x^{2}}{2}$, then $12\int x dx = 12\times\frac{x^{2}}{2}=6x^{2}$

Step3: Integrate $\int7dx$

Since $\int kdx=kx + C$ (where $k$ is a constant), for $k = 7$, $\int7dx=7x$

Step4: Combine the results

$\int(12x + 7)dx=6x^{2}+7x + C$

Answer:

$6x^{2}+7x + C$