Set u=3x-7
That means that du=3dx. However, you don't have a 3 on the top.
Don't worry. Instead, just multiply the integral by 3/3. That way, you have the 3 sufficient for the substitution.
Your equation becomes:
int (3 * 2)/(3 sqrt(3x-7))dx
You can then substitute u into the square root and du for 3dx using the three on the top. You should then get
int 2/(3 sqrtu)
Now personally, I like to take the 2/3 out from the integral and write sqrtu as u^(-1/2). Rewriting this, you get
2/3 int u^(-1/2)
Ignore the 2/3 for now and focus on the int u^(-1/2). Add 1 to the power and then multiply by 1/2 since that's the number you get from adding 1 to the power. Simplify and you should have:
(1/3)(u^(1/2)).
Now since u=3x-7, we need to plug that back into the result. Also, the power of 1/2 is the same thing as the square root. Plugging in and writing a square root, we should get:
(1/3)(sqrt(3x-7))
