Question

What is `int (x+7)dx`?

Answer 1

`intx+7dx=x^2/2+7x+C`

Explanation:

The Fundamental Theorem of Calculus states

`intf(x)dx=F(x)+C` where `F'(x)=f(x)`

Since `(x^2/2)'=x` by the power rule `intxdx=x^2/2`

and since `intcdx=cintdx` then `int7dx=7intdx=7x`

And since the integral of a sum is the sum of integrals

`intx+7dx=x^2/2+7x+C`