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evaluate ∫ (tan x + cot x)^2 dx

evaluate
∫ (tan x + cot x)^2 dx

Grade:12

2 Answers

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

I = \int (tanx+cotx)^2dx
I = \int (tan^2x+cot^2x+2)dx
I = \int (sec^2x-1+cosec^2x-1+2)dx
I = \int sec^2xdx+\int cosec^2xdx
I = tanx+\int cosec^2xdx
I = tanx - cotx + c
Kushagra Madhukar
askIITians Faculty 628 Points
2 years ago
Dear student,
Please find the answer to your problem below.
 
I = ∫ (tanx + cotx)2 dx
I = ∫ (tan2x + cot2x + 2) dx
I = ∫ (sec2x – 1 + cosec2x – 1 + 2) dx
I = ∫sec2x dx + ∫cosec2x dx
Hence, I = tanx – cotx + c
 
Hope it helps.
Thanks and regards,
Kushagra

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