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" 32."sec^(-1)((1+tan^(2)x)/(1-tan^(2)x)...

" 32."sec^(-1)((1+tan^(2)x)/(1-tan^(2)x))

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sec^-1((1+tan ^2x)/(1-tan ^2 x))

sec^-1((1+tan ^2x)/(1-tan ^2 x))

sec^(2)2x=1-tan2x

sec^(2)2x=1-tan2x

For any real number x ge 1 , the expression sec^(2)x ( tan^(-1)x) - tan^(2)x ( sec^(-1) x) is equal to

For any real number x ge 1 , the expression sec^(2) ( tan^(-1)x) - tan^(2) ( sec^(-1) x) is equal to

For any real number x ge 1 , the expression sec^(2) ( tan^(-1)x) - tan^(2) ( sec^(-1) x) is equal to

For any real number x ge 1 , the expression sec^(2) ( tan^(-1)x) - tan^(2) ( sec^(-1) x) is equal to

int(4sec^(2)x tan x)/(sec^(2)x+tan^(2)x)dx=log|1+f(x)|+C

int(1)/(sec^(2)x+2tan^(2)x)dx