I have this homework problems:
$$\int \dfrac{dx}{\sqrt{-x^2 + 3x - 4}}$$
What i did was take out $\sqrt{-1}$ from denominator, and complete square. The result I get was :
$$\dfrac{\ln\left|x+ \sqrt{x^2 - 3x + 4} -\frac{3}{2} \right|}{\sqrt{-1}}+C$$
But wolfram alfa gave me the following result:
$$\tan^{-1}\left(\dfrac{3-2x}{2\sqrt{-x^2 + 3x -4}}\right)+C$$
which doesn't involve $\sqrt{-1}$. I want to know how to proceed for integratin in such types of question.