Here's the question you clicked on:
suju101
integrate sin(tan^-1x)/(1+x^2). please help with the steps
Set u=arctan(x), so that du= 1/(1+x^2). Thus, using this u-substitution, the integral is equivalent to the integral of sin(u). Since the integral of sin(u) is -cos(u)+C, the final answer is just \[\sin (\tan^{-1} (x))+C\] Note also that sin(arctan(x)) is the same as \[x/\sqrt{x^2+1}\] So that function plus your constant of integration is also a correct solution.
Sorry, it should be \[-\cos (\tan^{-1} (x))+C\]
Also, that means that the alternate answer is instead \[1/\sqrt{x^2+1} + C\]