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Question
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
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Solution
Let I = `int sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Put `x^(3/2)` = t
∴ `(3)/(2) sqrt(x)*dx` = dt
∴ `sqrt(x)*dx = (2)/(3)*dt`
∴ I = `(2)/(3) int sec t tan t*dt`
= `(2)/(3)sec t + c`
= `(2)/(3) sec(x^(3/2)) + c`.
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