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int sqrt(x^2 - a^2) = 1/2 x sqrt (x^2 - ...

`int sqrt(x^2 - a^2) = 1/2 x sqrt (x^2 - a^2) - 1/2 a^2 log ( x + sqrt( x^2 - a^2) + c`

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`"Let I"=int sqrt(x^(2)-a^(2))dx =int sqrt(x^(2)-a^(2)). 1dx`
`=sqrt(x^(2)-a^(2)). int 1dx-int [(d)/(dx)(sqrt(x^(2)-a^(2))). int 1dx]dx`
`=sqrt(x^(2)-a^(2)).x-int (x)/(sqrt(x^(2)-a^(2))).dx`
`=x.sqrt(x^(2)-a^(2))-int (x^(2)-a^(2)+a^(2))/(sqrt(x^(2)-a^(2)))dx `
`=xsqrt(x^(2)-a^(2))-int sqrt(x^(2)-a^(2))dx-a^(2) int (dx)/(sqrt(x^(2)-a^(2)))`
`=xsqrt(x^(2)-a^(2))-I-a^(2)log|x+sqrt(x^(2)-a^(2))|`
`therefore 2I=xsqrt(x^(2)-a^(2))-a^(2)log |x+sqrt(x^(2)-a^(2))|`
`therefore I=(x)/(2)sqrt(x^(2)-a^(2))-(a^(2))/(2)log|x+sqrt(x^(2)-a^(3))|+c`
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