2.3 Problem number 250

$$\int \frac{1}{b\cos (x)+a\sin (x)}dx$$

Optimal antiderivative $$-\frac{\mathrm{arctanh}\left(\frac{a\cos \left(x\right)-b\sin \left(x\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}$$

command

integrate(1/(b*cos(x)+a*sin(x)),x)

Sympy 1.10.1 under Python 3.10.4 output

$$\text{Exception raised: AttributeError}$$

Sympy 1.8 under Python 3.8.8 output

$$\{\begin{array}{ll}\tilde{\mathrm{\infty }}(-\log (\tan \left(\frac{x}{2}\right)-1)+\log (\tan \left(\frac{x}{2}\right)+1))& \text{for}a=0\wedge b=0\\ \frac{\log (\tan \left(\frac{x}{2}\right))}{a}& \text{for}b=0\\ \frac{1}{b\sin \left(x\right)+i\sqrt{b^2}\cos \left(x\right)}& \text{for}a=-\sqrt{-b^2}\\ \frac{1}{b\sin \left(x\right)-i\sqrt{b^2}\cos \left(x\right)}& \text{for}a=\sqrt{-b^2}\\ -\frac{\log (-\frac{a}{b}+\tan \left(\frac{x}{2}\right)-\frac{\sqrt{a^2+b^2}}{b})}{\sqrt{a^2+b^2}}+\frac{\log (-\frac{a}{b}+\tan \left(\frac{x}{2}\right)+\frac{\sqrt{a^2+b^2}}{b})}{\sqrt{a^2+b^2}}& \text{otherwise}\end{array}$$