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Please give full solutionAnd how can we know that which function is integrable

Please give full solutionAnd how can we know that which function is integrable

Question Image
Grade:12th pass

1 Answers

Ritika Das
105 Points
4 years ago
We have I=∫sqrt.(1+tan x).dx.
Let u=1+tan x.
du/dx=sec2x.
dx=(1/sec2x).du.
Now putting the values we have I=∫sqrt.(u).du.(1/sec2x).
or, I=(1/sec2x)∫(u)1/2.du.
or, I=(1/sec2x).(2/3).(u)3/2 + c.
Putting back value of u we get the final answer: – 
I = (2/3sec2x).(1+tan x)3/2 + c.
Please approve my answer if you like the explanation! 
Regards.

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