Question

Evaluate $\int (1-x)\left(2+3x\right)dx=$

Answer 1

Consider the given integral.

$I=\int (1-x)(2+3x)dx$

$I=\int (2+3x-2x-3x^2)dx$

$I=\int (2+x-3x^2)dx$

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

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

Hence, the value of integral is $2x+\frac{x^2}{2}-x^3+C$.