Question

3. хгех

Answer 1

The given integral is given below as,

I= ∫ x 2 e x dx

Use integration by parts rule. Consider x 2 as first function and e x as second function.

I= ∫ x 2 e x dx = x 2 ∫ e x dx − ∫ ( d dx x 2 ∫ e x dx ) dx = x 2 e x −2 ∫ x e x dx

Again by using integration by parts, we get

I= x 2 e x −2[ x ∫ e x dx − ∫ ( d dx x ∫ e x dx )dx ] = x 2 e x −2[ x e x − ∫ e x dx ] = x 2 e x −2x e x +2 e x +C I=( x 2 −2x+2 ) e x +C

Thus, the integration of ∫ x 2 e x dx is ( x 2 −2x+2 ) e x +C.