Question

find \\( \int (6x + 7)dx \\).\\( \int (6x + 7)dx = \square \\)

Explanation:

Step1: Apply Sum Rule of Integration

The integral of a sum is the sum of the integrals, so $\int (6x + 7)dx=\int 6x dx+\int 7 dx$.

Step2: Integrate $6x$

Using the power rule $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ (for $n
eq - 1$), for $\int 6x dx$, we have $6\times\frac{x^{1 + 1}}{1+1}=6\times\frac{x^{2}}{2}=3x^{2}$.

Step3: Integrate 7

The integral of a constant $k$ is $kx + C$, so $\int 7 dx=7x + C$.

Step4: Combine Results

Adding the two results together, we get $3x^{2}+7x + C$.

Answer:

$3x^{2}+7x + C$