∫√(tanx)dx?

Question

please solve....

Answer 1

Using the substitution

 

Now, I will process the integral so that dv appears in it.

Substitute the   and   above form.

Answer 2

continuous.....

Now this is starting to get tricky, so I'll break the first term into two integrals I₁ and I₂, and the

second term into two more integrals I₃ and I₄.

Now I'll do each of I₁, I₂, I₃, and I₄ separately:

This integral is of the form ∫du/u, which is ln|u|, so

This can be converted into the form a / [(av+b)²+1] , if we let a =sqrt(2) and b =-1

This integral is of the form ∫du/u, which is ln|u|, so

This can be converted into the form a /[(av+b)²+1], if we let a = sqrt(2) and b = -1

Substitute the in I₁, I₂, I₃, and I₄.

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