The answer will the the value of the definite integral:
Since integrals of powers of x are simple, I am going to rewrite the second term as the appropriate power of x:
Next we can use a property of integrals that tells us the the integral of a sum is the same as the sum of the integrals:
Next we can factor out the 4 in the first integral using a property of integrals:
Each integral is now a power of x. In general . Using this on both of our integrals we get: evaluated from x=1 to x=4
This simplifies as follows: evaluated from x=1 to x=4 evaluated from x=1 to x=4
Evaluating this expression from 1 to 4:
Simplifying: