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find-dx-1-x-2-1-x-2-




Question Number 41846 by maxmathsup by imad last updated on 13/Aug/18
find  ∫     (dx/( (√(1+x^2  ))  +(√(1−x^2 ))))
finddx1+x2+1x2
Answered by MJS last updated on 13/Aug/18
∫(dx/( (√(1+x^2 ))+(√(1−x^2 ))))=(1/2)∫((√(1+x^2 ))/x^2 )dx−(1/2)∫((√(1−x^2 ))/x^2 )dx=       [both integrals by parts]  =(1/2)(arcsin x +arcsinh x)+(((√(1−x^2 ))−(√(1+x^2 )))/(2x))+C
dx1+x2+1x2=121+x2x2dx121x2x2dx=[bothintegralsbyparts]=12(arcsinx+arcsinhx)+1x21+x22x+C
Commented by math khazana by abdo last updated on 14/Aug/18
thank you sir.
thankyousir.

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