Question

solve the following


$\int\limits {\frac{dx}{x^{2}-a^{2} } }$

Answer 1

Step-by-step explanation:

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Answer 2

$\int\limits {\frac{dx}{x^{2}-a^{2} } }$

$let \: a \: sec \alpha = x$

$\frac{dx}{d \alpha } = a \sec\alpha \tan\alpha$

$dx \: = a \sec( \alpha ) \tan( \alpha ) d \alpha$

$\int\limits {a\frac{ \sec \alpha \tan\alpha d \alpha }{ {a}^{2} { \tan( \alpha ) }^{2} } }$

$\int\limits {\frac{ \sec( \alpha ) dx}{ a\tan( \alpha ) } }$

$\int\limits {\frac{d \alpha }{a \sin( \alpha ) } }$

$\int\limits {{ \csc( \alpha )/a d \alpha }{} }$

$log( \csc( \alpha ) - \cot( \alpha ) )/a + c$