# Question 745b7

Mar 26, 2017

$y = \frac{2}{7} {x}^{7} - \frac{1}{6} {x}^{6} - \frac{3}{2} {x}^{4} + {x}^{3} + c$

#### Explanation:

I am assuming you require to find the function y

$\textcolor{b l u e}{\text{integrate " y'" to obtain y}}$

distribute the brackets.

$\Rightarrow \left({x}^{5} - 3 {x}^{2}\right) \left(2 x - 1\right)$

$= 2 {x}^{6} - {x}^{5} - 6 {x}^{3} + 3 {x}^{2}$

Integrate each term using the $\textcolor{b l u e}{\text{power rule}}$

• int(ax^n)=a/(n+1)x^(n+1) ; n!=-1#

$\Rightarrow y = \int \left(2 {x}^{6} - {x}^{5} - 6 {x}^{3} + 3 {x}^{2}\right) \mathrm{dx}$

$\textcolor{w h i t e}{\Rightarrow y} = \frac{2}{7} {x}^{7} - \frac{1}{6} {x}^{6} - \frac{3}{2} {x}^{4} + {x}^{3} + c$

where c is the constant of integration.