\( \int f(g(x)) g^{\prime}(x) d x=\int f(t) d t \) where \( t=g(x) \). This rule is called subst....

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PW Solutions
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Counter-Strike: Source
Game:
Counter-Strike: Source (2004)
Duration: 4:07
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\( \int f(g(x)) g^{\prime}(x) d x=\int f(t) d t \) where \( t=g(x) \). This
\( \mathrm{P} \)
rule is called substitution rule. Answer the
W.
following questions:
\[
\int \frac{x^{2}-1}{x^{2}+1} \frac{d x}{\sqrt{1+x^{4}}}=
\]
(1) \( \frac{1}{\sqrt{2}} \operatorname{Cosh}^{-1} \frac{x \sqrt{2}}{1+x^{2}}+c \)
(2) \( \frac{1}{\sqrt{2}} \operatorname{Sinh}^{-1} \frac{x \sqrt{2}}{1+x^{2}}+c \)
(3) \( \frac{1}{\sqrt{2}} \operatorname{Tan}^{-1}\left(\frac{x \sqrt{2}}{1+x^{2}}\right)+c \)
(4) \( \frac{1}{\sqrt{2}} \operatorname{Cos}^{-1} \frac{x \sqrt{2}}{1+x^{2}} \)
.


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