∫x sec(x)32tan(x)32dx - Mathematics and Statistics

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Sum

`int sqrt(x)  sec(x)^(3/2) tan(x)^(3/2)"d"x`

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Solution

Let I = `int sqrt(x)*sec(x^(3/2))*tan(x^(3/2))"d"x`

Put `x^(3/2)` = t

∴ `3/2x^(1/2)  "d"x` = dt

∴ `sqrt(x)  "d"x = 2/3  "dt"`

∴ I = `2/3  int sec "t"*tan"t"* "dt"`

= `2/3  sec "t" + "c"`

∴ I = `2/3  sec(x^(3/2)) + "c"`

  Is there an error in this question or solution?
Chapter 2.3: Indefinite Integration - Very Short Answers

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