Evaluate the integral of the quotient of the secant squared of x and the square root of the quantity 1 plus tangent x, dx.

https://gyazo.com/56a83617dc456d74002487417af5f68a

Question

Evaluate the integral of the quotient of the secant squared of x and the square root of the quantity 1 plus tangent x, dx.



https://gyazo.com/56a83617dc456d74002487417af5f68a

retireed · Answer

Nice.  I just started reviewing by calculus yesterday, after my last class was in 1977, yes the year.  I am still practicing Calc I.      So sorry, I'm to rusty for something this advance.

anonymous · Answer

Refer to the attachment from Mathematica v9, home edition:

idku · Answer

what is up with this attachement?
If you don't know how to help the user don't just post the solution with answer from mathematica like this, because that's inapropriate.

idku · Answer

Of course the steps are right and the quickest (mathematica, dah), but if you still need help or have questions, then reply.

anonymous · Answer

Please explain how it was done.

anonymous · Answer

Recall that $\dfrac{\mathrm{d}}{\mathrm{d}x}\tan x=\sec^2x$, so a substitution of $u=\tan x$ would make things simpler:
$$\int\frac{\sec^2x}{\sqrt{1+\tan x}}\,\mathrm{d}x\stackrel{u\tan x}{=}\int \frac{\mathrm{d}u}{\sqrt{1+u}}$$