What is int (x+7)dx?

Jan 28, 2017

$\int x + 7 \mathrm{dx} = {x}^{2} / 2 + 7 x + C$

Explanation:

$\int f \left(x\right) \mathrm{dx} = F \left(x\right) + C$ where $F ' \left(x\right) = f \left(x\right)$

Since $\left({x}^{2} / 2\right) ' = x$ by the power rule $\int x \mathrm{dx} = {x}^{2} / 2$

and since $\int c \mathrm{dx} = c \int \mathrm{dx}$ then $\int 7 \mathrm{dx} = 7 \int \mathrm{dx} = 7 x$

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

$\int x + 7 \mathrm{dx} = {x}^{2} / 2 + 7 x + C$