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Integrate from (pi)/6 to (pi)/3 ∫dx/(1+tan 5 x)

Integrate from (pi)/6 to (pi)/3
∫dx/(1+tan5x)

Grade:12

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int_{\pi /6}^{\pi /3}\frac{1}{tan^{5}x + 1}dx…......(1)
I = \int_{\pi /6}^{\pi /3}\frac{1}{tan^{5}(\frac{\pi }{2}-x) + 1}dx
I = \int_{\pi /6}^{\pi /3}\frac{1}{cot^{5}x + 1}dx
I = \int_{\pi /6}^{\pi /3}\frac{tan^{5}x}{tan^{5}x+1}dx….......(2)
(1) + (2)
2I = \int_{\pi /6}^{\pi /3}\frac{1+tan^{5}x}{tan^{5}x+1}dx
2I = \int_{\pi /6}^{\pi /3}1.dx
2I =[x]_{\pi /6}^{\pi /3}
2I =\frac{\pi }{3} - \frac{\pi }{6}
2I =\frac{\pi }{6}
I =\frac{\pi }{12}
Lovey
10 Points
6 years ago
Thanx.

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