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Question
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Solution
Let I = `int(x^n - 1)/sqrt(1 + 4x^n).dx`
Put xn = t
∴ nxn–1 dx = dt
∴ xn–1 dx = `dt/n`
∴ I = `int (1)/sqrt(1 + 4t).dt/n`
= `(1)/nint(1 + 4t)^(-1/2)dt`
= `1/n.((1 + 4t)^(1/2))/(1/2) xx (1)/(4) + c`
= `(1)/(2n).sqrt(1 + 4x^n) + c`.
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