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Integrate the following integeandPlease reply soon!!!!!!!

Integrate the following integeandPlease reply soon!!!!!!!

Question Image
Grade:12

1 Answers

Ritika Das
105 Points
4 years ago
 
Let u = tan x.
du/dx = sec2x.
dx = (1/sec2x).du.
I = ∫(sec x)x/(sqrt(tan x)).dx
Now replacing tan x with u and dx with (1/sec2x).du we get I: – 
I = ∫(sec x)x/(sqrt(u)).du.(1/sec2x).
  = secx – 2x∫u-1/2.du.
  = 2secx – 2x.u1/2 + c
Replacing u with tan x,
I = 2secx – 2x.(sqrt(tan x)) + c. 
Please approve my answer if you liked the explanation!

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