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Consider the following statements :
\( \mathrm{S}_{1} \) : The antiderivative of every even function is an odd function.
\( \mathrm{P} \)
\( \mathbf{S}_{2} \) : Primitive of \( \frac{3 x^{4}-1}{\left(x^{4}+x+1\right)^{2}} \) w.r.t. \( x \) is \( \frac{x}{x^{4}+x+1}+C \).
W
\( -\mathbf{S}_{3}: \quad \int \frac{1}{\sqrt{\sin ^{3} x \cos x}} d x=\frac{-2}{\sqrt{\tan x}}+C \)
\( \mathbf{S}_{4} \) : The value of \( \int\left(\sqrt{\frac{a+x}{a-x}}-\sqrt{\frac{a-x}{a+x}}\right) d x \) is equal to \( -2 \sqrt{a^{2}-x^{2}}+C \)
State, in order, whether \( \mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}, \mathrm{~S}_{4} \) are true or false
(A) FFTT
(B) TTTT
(C) FFFF
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