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

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PW Solutions
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Published on ● Video Link: https://www.youtube.com/watch?v=CMnQXDGoqNQ


Counter-Strike: Source
Game:
Counter-Strike: Source (2004)
Duration: 6:28
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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:
\[
\int \frac{d x}{(x+1)^{3} \sqrt{x^{2}+2 x-3}}=\frac{\sqrt{x^{2}+2 x-3}}{8(x+1)^{2}}-\frac{1}{16} f(x)+c
\]
then \( f(x) \) is equal to
(1) \( \sin ^{-1}\left(\frac{2}{x+1}\right) \)
(2) \( \cos ^{-1}\left(\frac{x+1}{2}\right) \)
(3) \( \sin ^{-1}\left(\frac{x+1}{2}\right) \)
(4) \( \sec ^{-1}\left(\frac{x+1}{2}\right) \)
.


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