Question

Solve the following : `int_2^4 x/(x^2 + 1)*dx`

Answer 1

Let I = `int_2^4 x/(x^2 + 1)*dx`

Put x² + 1 = t
∴ 2x·dx = dt
∴ x·dx = `"dt"/(2)`
When x = 2, t = 2² + 1 = 5
When x = 4, t = 42 + 1 = 17

∴ I = `int_5^17 (1)/"t"*"dt"/2`

= `(1)/(2) int_5^17 "dt"/"t"`

= `(1)/(2)[log|"t"|]_5^17`

= `(1)/(2)(log 17 - log 5)`

∴ I = `(1)/(2)log (17/5)`.