How do I integrate the following: \(\displaystyle\int{\frac{{\sqrt{{{\tan{{a}}}{x}}}}}{{{1}+\sqrt{{{\tan{{a}}}{x}}}}}}{\left.{d}{x}\right.}\)

Elijah Schwartz

Elijah Schwartz

Answered question

2022-04-13

How do I integrate the following:
tanax1+tanaxdx

Answer & Explanation

folytonr4qx

folytonr4qx

Beginner2022-04-14Added 14 answers

Hint:
Substituting u=ax, gives us:
I=tanax1+tanaxdx
I=1atanu1+tanudu
aI=du1tanu+1du
Now the second integral cam be written as:
I1=11+tanudu
=2v1v((v1)4+1)dv
after substituting v=1+tanu
The next step is obviously a PFD

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