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Integral Calculus
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| +khello...........
{tan^2x+2}^1/2={sec^2x+1}^1/2
={sec^2x+1}/{sec^2x+1}^1/2
=sec^2x/{sec^2x +1}^1/2 + 1/{sec^2x+1}^1/2
=sec^2x/{tan^2x +2}^1/2 + cosx/{1+cos^2x}^1/2
=sec^2x/{tan^2x +2}^1/2 + cosx/{2-sin^2x}^1/2 =f{x}
now for integral f{x}dx for first term put tanx =t ,for second term put sinx =t and integrate
am i correct ???????????????
integration of root of (tan^2 x+2)
let the thing inside the integral=t^2...make this substituton and solve furthur to get...
t^2 dt/ (t^2 -2)^1/2 * (t^2 -1)...
now make a substitution as...(t^2 -2)=u^2...
sove the expression to get ... (u^2 + 2)^(1/2 )/ u^2 +1..
now rationalize the root expression and divide Nr BY Dr to get a simplified expression which can be integrated easily...
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