find the most general antiderivative or indefinite integral. ∫(12x + 5)dx ∫(12x + 5)dx =

Explanation:

Step1: Use integral sum - rule

$\int(12x + 5)dx=\int12x dx+\int5dx$

Step2: Use constant - multiple rule for integrals

$\int12x dx+\int5dx = 12\int xdx+5\int dx$

Step3: Apply power - rule for integrals $\int x^n dx=\frac{x^{n + 1}}{n+1}+C(n\neq - 1)$ and $\int dx=x + C$

$12\times\frac{x^{1 + 1}}{1+1}+5x+C$ $12\times\frac{x^{2}}{2}+5x+C$ $6x^{2}+5x+C$

Answer:

$6x^{2}+5x+C$