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Question
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
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Solution
Put 1 + x2 = u
2x dx = du
x dx = `1/2 "du"`
`int x/sqrt(1 + x^2) "d"x = int (1/2 "du")/sqrt("u")`
= `1/2 int "u"^(- 1/2) "du"`
= `1/2 ("u"^(- 1/2 + 1))/(- 1/2 + 1) + "c"`
= `1/2 ("u"^(1/2))/(1/2) + "c"`
= `(1 + x^2)^(1/2) + "c"`
`int x/sqrt(1 + x^2) "d"x = sqrt(1 + x) + "c"`
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