# What is int 4 x^5 -7 x^4 + 3 x^3 -8 x^2 -4 x + 1 dx?

Jan 9, 2016

$\frac{2}{3} {x}^{6} - \frac{7}{5} {x}^{5} + \frac{3}{4} {x}^{4} - \frac{8}{3} {x}^{3} - 2 {x}^{2} + x + C$

#### Explanation:

Use the power rule in reverse:

$\int {x}^{n}$ $\mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + C$

Thus, the antiderivative of the function is

$\frac{4}{6} {x}^{6} - \frac{7}{5} {x}^{5} + \frac{3}{4} {x}^{4} - \frac{8}{3} {x}^{3} - \frac{4}{2} {x}^{2} + x + C$

which simplifies to be

$\frac{2}{3} {x}^{6} - \frac{7}{5} {x}^{5} + \frac{3}{4} {x}^{4} - \frac{8}{3} {x}^{3} - 2 {x}^{2} + x + C$