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# ϕ@1/(a^2+x^2)

$3\displaystyle{\int \frac{\hspace{2}1\hspace{2}}{\hspace{2} {a}^{2}+{x}^{2} \hspace{2}}dx }$@@$3\displaystyle{ \( a\neq 0 \) }$
$3\displaystyle{x=a\tan t\text{\hspace{5}} \( - \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}}< t< \frac{\hspace{2}{\pi}\hspace{2}}{\hspace{2}2\hspace{2}} \) }$ ƂsDƁC
$3\displaystyle{\frac{\hspace{2} dx \hspace{2}}{\hspace{2} dt \hspace{2}}=\frac{\hspace{2}a\hspace{2}}{\hspace{2} { \cos }^{2}t \hspace{2}}\rightarrow dx=\frac{\hspace{2}a\hspace{2}}{\hspace{2} { \cos }^{2}t \hspace{2}}dt}$

 ^ $3\displaystyle{=\int \frac{\hspace{2}1\hspace{2}}{\hspace{2} {a}^{2}+{a}^{2}{ \tan }^{2}t \hspace{2}}\cdot \frac{\hspace{2}a\hspace{2}}{\hspace{2} { \cos }^{2}t \hspace{2}}dt }$ @ @ @ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2}a\hspace{2}}\int \frac{\hspace{2}1\hspace{2}}{\hspace{2} 1+{ \tan }^{2}t \hspace{2}}\cdot \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \cos }^{2}t \hspace{2}}dt }$ @ @ @ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2}a\hspace{2}}\int { \cos }^{2}t\cdot \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \cos }^{2}t \hspace{2}}dt }$ @ $3\displaystyle{ \( {}^\bullet\limits{ }_\bullet {}^\bullet 1+{ \tan }^{2}t=\frac{\hspace{2}1\hspace{2}}{\hspace{2} { \cos }^{2}t \hspace{2}} \) }$ @ @ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2}a\hspace{2}}\int dt }$ @ @ @ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2}a\hspace{2}}t+C}$ @ C:ϕ萔@@ @ $3\displaystyle{=\frac{\hspace{2}1\hspace{2}}{\hspace{2}a\hspace{2}}{\tan }^{ - 1 }\frac{\hspace{2}x\hspace{2}}{\hspace{2}a\hspace{2}}+C}$ @

z[>>JeS[>>ϕ>>{ƂȂ֐̐ϕ>>ϕ@1/(a^2+x^2)

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