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Question
Evaluate: `int x/(x^2 + 1)"d"x`
Options
2log(x2 + 1) + c
`1/2`log(x2 + 1) + c
`"e"^(x^2 + 1) + "c"`
`logx + x^2/2 + "c"`
Solution
`bb(1/2log(x^2 + 1) + c)`
Explanation:
`int x/(x^2 + 1)"d"x`
= `1/2 int "dt"/"t"`
= `1/2 log "t" + "C"`
= `1/2 log (x^2 + 1) + "C"`
Put x2 + 1 = t
2x dx = dt
x dx = `"dt"/2` ...(i)
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