To find the integral of a function, we can use the power rule of integration. According to the power rule, the integral of x^n with respect to x is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.
In this case, we have a constant function, 15. So the integral of 15 dx will be 15x + C, where C is the constant of integration.
Now, let's find the integral of 15 dx over the given interval from x+1 to 2x+8.
The integral of 15 dx from x+1 to 2x+8 can be calculated as follows:
∫(x+1, 2x+8) 15 dx = [15x] evaluated from x+1 to 2x+8
To evaluate the integral, we substitute the upper limit (2x+8) and lower limit (x+1) into the function 15x:
[15(2x+8)] - [15(x+1)]
Simplifying the expression, we have:
30x + 120 - 15x - 15
Combining like terms, we get:
15x + 105
Therefore, the integral of 15 dx from x+1 to 2x+8 is 15x + 105.