Annoying quadratic cotangent in integral

[Stereotypical]

Hello. Please help me with this integral:

\(\displaystyle \int_{\frac{\pi}{4}}^{\frac{\pi}{2}}\sqrt {1 + cot^{2}(x)}\,\mathrm{d}x \)

 

[soroban]

Hello, Stereotypical!

\(\displaystyle \text{Please help me with this integral:}\)

. . \(\displaystyle \displaystyle \int_{\frac{\pi}{4}}^{\frac{\pi}{2}}\sqrt {1 + \cot^2x}\,dx \)

Use the identity: .\(\displaystyle 1 + \cot^2\!\theta \:=\:\csc^2\!\theta\)

 

[Stereotypical]

Hello, Stereotypical!


Use the identity: .\(\displaystyle 1 + \cot^2\!\theta \:=\:\csc^2\!\theta\)

That did it, thank you so much!