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imperialist
 3 years ago
Best ResponseYou've already chosen the best response.3Set u=arctan(x), so that du= 1/(1+x^2). Thus, using this usubstitution, 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.

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.3Sorry, it should be \[\cos (\tan^{1} (x))+C\]

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.3Also, that means that the alternate answer is instead \[1/\sqrt{x^2+1} + C\]
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