CBSE Class 12-commerce Answered

Let I = I₁ + I₂

where I₁ and I₂ are defined as

   and  

Let us solve the first integration I₁ .

Let  u = ⁴√x = x^1/4 ;  

du = (1/4) x^-3/4 dx = (1/4) u^-3 dx

dx = 4 u³ du

Hence the first integration I₁ is

we can write the integrand function as

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Let us solve the second integration

where I₃ is

Let v = √x  ;

dv = dx/ ( 2 √x ) ;

dx = 2 u du

I₃ = 2 u - 2 log(1+u )

I₃  = 2 √x - ln( 1 + √x )²

Hence the complete integration is

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