Question

Evaluate: $\int e^x(x^2+2x)dx$

Answer 1

Now,

$\int e^x(x^2+2x)dx$

$=\int e^x{x}^{2}dx$$+\int e^x\left(2x\right)dx$

$=e^x.x^2$$-\int e^x\left(2x\right)dx$$+\int e^x\left(2x\right)dx+c$ [ Using method of by parts] [ Where $c$ is integrating constant]

$=x^2{e}^x+c$