How do I integrate sinx/(1+cos^2(x))? I think I should use the following rule: integration of dx/a^2 + x^2 with a = 1 and x = cos x. That would give me an answer of tan^-1 cos x. Is that right?
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∫ (sinx)/(1+cos^2(x)) dx
Let u = cos(x)
du = -sin(x) dx
dx = -1/sin(x) du
- ∫ (1)/(1+u^2) du
-arctan(u)
-arctan(cos(x)) + C <--- Note the negative
Done!
Let u = cos(x)
du = -sin(x) dx
dx = -1/sin(x) du
- ∫ (1)/(1+u^2) du
-arctan(u)
-arctan(cos(x)) + C <--- Note the negative
Done!