Evaluate:\(\int\cfrac{dx}{(x^2+16)}\)∫ dx/(x2+16)

1.	Evaluate:\(\int\cfrac{dx}{(x^2+16)}\)∫ dx/(x2+16)
Answer» To find: \(\int\frac{dx}{(x^2+16)}\) Formula Used: \(\int\cfrac{dx}{a^2+x^2}=\frac{1}{a}tan^{-1}(\frac{x}{a})+c\) Rewriting the given equation, \(\Rightarrow\)\(\int\frac{dx}{4^2+x^2}\) Here a = 4 \(\Rightarrow\)\(\cfrac{1}{4}\times tan^{-1}(\frac{x}{4})+c\) Therefore, \(\int\cfrac{dx}{(x^2+16)}=\frac{1}{4}\times tan^{-1}(\frac{x}{4})+c\)\(\)

Answer»

To find: \(\int\frac{dx}{(x^2+16)}\)

Formula Used: \(\int\cfrac{dx}{a^2+x^2}=\frac{1}{a}tan^{-1}(\frac{x}{a})+c\)

Rewriting the given equation,

\(\Rightarrow\)\(\int\frac{dx}{4^2+x^2}\)

Here a = 4

\(\Rightarrow\)\(\cfrac{1}{4}\times tan^{-1}(\frac{x}{4})+c\)

Therefore,

\(\int\cfrac{dx}{(x^2+16)}=\frac{1}{4}\times tan^{-1}(\frac{x}{4})+c\)\(\)

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