How do you integrate int (x^3+2)dx?

Nov 1, 2016

$\int \left({x}^{3} + 2\right) \mathrm{dx} = {x}^{4} / 4 + 2 x + c$

Explanation:

Using the power rule of integration, $\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + c ,$

$\int \left({x}^{3} + 2\right) \mathrm{dx} = \int \left({x}^{3} + 2 {x}^{0}\right)$

$= {x}^{3 + 1} / \left(3 + 1\right) + \frac{2 {x}^{1}}{1} + c$

$= {x}^{4} / 4 + 2 x + c$

• Remember to add the constant c, since this is an indefinite integral and constants are removed when the primitive is derived.
Nov 1, 2016

$\int {x}^{3} + 2 \mathrm{dx}$

$= \frac{{x}^{3 + 1}}{3 + 1} + 2 x + C$

$= \frac{1}{4} {x}^{4} + 2 x + C$

This is because:

$\int {x}^{n} \mathrm{dx}$

$= \frac{{x}^{n + 1}}{n + 1} + C$

And also:

$\int k \mathrm{dx}$

$= k x + C$