Integrasikan log(1+tan x) dari 0 hingga pi/4.

Penyelesaian:

Mari kita pertimbangkan

(I = int_0^{pi/4} log(1+tanx)dx)

Kita tahu itu

(int_0^af(x)dx=int_0^af(ax)dx)

(I = int_0^{pi/4}log(1+tan[{frac{pi}{4}}-x]dx)

(I = int_0^{pi/4}log(1 + frac{1-tanx}{1+ tanx})dx)

(I = int_0^{pi/4}log(frac{2}{1+ tanx})dx)

(I = int_0^{pi/4}log, 2dx – int_0^{pi/4} log, (1 + tanx)dx)

(I = int_0^{pi/4}log, 2dx – I)

(2I = int_0^{pi/4}log, 2dx)

(I = log, 2times frac{pi }{4}times frac{1}{2})

(I = frac{pi }{8}log, 2)

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