Question

Evaluate: `int dx/(x + x^-10)`.

Answer 1

Let I = `int dx/(x + x^-10)`

= `int dx/(x + (1/x^10))`

= `int (x^10)/(x^11 + 1) dx`

Put x¹¹ + 1 = t

∴ 11x¹⁰ dx = dt

∴ `x^10 dx = 1/11 dt`

∴ I = `int 1/t * 1/11 dt`

= `1/11 int 1/t dt`

= `1/11 log |t| + c`

= `1/11 log |x^11 + 1| + c`