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

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