Question

I= $\int \left(1-x\right)\left(2+3x\right)\left(5-4x\right)dx$

Answer 1

$\begin{array}{c}\int \left(1-x\right)\left(2+3x\right)\left(5-4x\right)dx\\ =\int \left(10-3x-19x^2+12x^3\right)dx\\ =10\int dx-3\int xdx-19\int x^{2}dx+12\int x^{3}dx\\ =10x-3.\frac{x^2}{2}-19.\frac{x^3}{3}+12.\frac{x^4}{4}+C\\ =10x-\frac{3x^2}{2}-\frac{19x^3}{3}+3x^4+C.\end{array}$