Question

how do you integrate for \[\sin (x/2)/(1+\cos (x/2))^3\]

Answer 1

substitute\[u = 1 + \cos \left( \frac{x}{2} \right)\]

Answer 2

is this the answer\[1/ [-2(1+\cos (x/2))^2] ?\]

Answer 3

the -2 should cancel

Answer 4

cancel wha tdo you mean?

Answer 5

\[u = 1 + \cos \left( \frac{x}{2} \right)\]\[du = -\frac{1}{2}\sin \left( \frac{x}{2} \right)dx\]\[\sin \left( \frac{x}{2} \right)dx=-2du\]substitute,\[\int\limits \frac{\sin \left( \frac{x}{2} \right)}{\left( 1+\cos \left( \frac{x}{2} \right) \right)^{3}}dx\]\[=-2 \int\limits\frac{1}{u^{3}}du\]

Answer 6

there wont be any -2 in the answer