# How do you find the indefinite integral of int (5t^8-2t^4+t+3)dt?

Nov 8, 2017

$\frac{5}{9} {t}^{9} - \frac{2}{5} {t}^{5} + \frac{1}{2} {t}^{2} + 3 t + c$

#### Explanation:

$\text{integrate each term using the "color(blue)"power rule}$

•color(white)int(ax^n)=a/(n+1)x^(n+1)to(n!=-1)

$\Rightarrow \int \left(5 {t}^{8} - 2 {t}^{4} + t + 3\right) \mathrm{dt}$

$= \frac{5}{9} {t}^{9} - \frac{2}{5} {t}^{5} + \frac{1}{2} {t}^{2} + 3 t + c$

$\text{where c is the constant of integration}$