Question

Integrate the ∫1/x^2-6x+11 dx from -5 to 5?

Answer 1

`int_(-5)^5(1/x^2-6x+11)dx=109.6`

Explanation:

As `intx^ndx=x^(n+1)/(n+1)`

and when `n=-1`, we have `intx^(-1)dx=int(dx)/x=lnx`

`int_(-5)^5(1/x^2-6x+11)dx`

= `int_(-5)^5(x^(-2)-6x+11)dx`

= `[x^(-1)/(-1)-6*x^2/2+11x]_(-5)^5`

= `[-1/x-3x^2+11x]_(-5)^5`

= `[(-1/5-3*5^2+11*5)-(-1/(-5)-3*(-5)^2+11*(-5))]`

= `[-0.2-75+55-0.2+75+55]`

= `109.6`