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Question

Evaluate : π/3π/611+tanxdx.

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Solution

Let I=x/3x/6dx1+tanxI=π/3x/6dx1+tan(π6+π3x)[Byusing property baf(x)dx=baf(a+bx)dx](i)I=π/3π/6dx1+tan(π2x)I=π/3π/6dx1+1cos2=π/3π/6dx1+cotxI=π/3π/6tanx1+tanxdx

Adding (i) and (ii), we get
2I=π/3π/6(1+tanx)(1+tanx)dx=π/3π/6dx=[x]π/3x/6=π3π6=π62I=π6 or I=π12

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