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Question
`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"`
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