Question

`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to ______.

Options

• `4/5`

• `5/4`

• `4/3`

• `3/4`

Answer 1

`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to `underlinebb(4/3)`.

Explanation:

`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx`

= `int_-1^1 (17x^5 + 29x^3 - 31x)/ubrace(x^2 + 1)_"Odd function" dx - int_-1^1  ubrace((x^4 - 1)/(x^2 + 1))_"Even function" dx`

= `0 - 2 int_0^1 ((x^2 - 1)(x^2 + 1))/((x^2 + 1)) dx`

= `-2[(x^3/3 - x)]_0^1`

= `4/3`