Integration using substitution

[james_s]

How do you do this, been on this for ages:

Use the substitution u = tan x to find the value of

Integral 1+tan^2 (x)/ 1-tan^2 (x) dx between 1/6 pi and 0,

Giving your answer in logarithmic form.


Thanks

 

[Deleted member 4993]

How do you do this, been on this for ages:

Use the substitution u = tan x to find the value of

Integral 1+tan^2 (x)/ 1-tan^2 (x) dx between 1/6 pi and 0,

Giving your answer in logarithmic form.


Thanks

What are your thoughts?

Please share your work with us ...even if you know it is wrong

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[stapel]

Use the substitution u = tan x to find the value of

Integral 1+tan^2 (x)/ 1-tan^2 (x) dx between 1/6 pi and 0

As posted, the integrand is this:

. . . . .\(\displaystyle 1\, +\, \dfrac{\tan^2(x)}{1}\, -\, \tan^2(x)\)

Would it be correct to assume that you meant (1 + tan²(x)) / (1 - tan²(x)), which typesets as follows?

. . . . .\(\displaystyle \dfrac{1\, +\, \tan^2(x)}{1\, -\, \tan^2(x)}\)

...been on this for ages:

Then you've got loads of work you can show. Please reply with this information. Thank you! :wink: