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Integrate x²-1/√x4+x²+1dx Someone pls Help Me..... To solve this problem

Integrate x²-1/√x4+x²+1dx Someone pls Help Me..... To solve this problem

Grade:12

1 Answers

sohaibchoudhary
11 Points
3 years ago

At the first taking expression and simplyfing it..

(x^2+1)/x^4+x^2+1

Dividing by x^2 in numerator and denominator. So it's become

=1+1/x^2 whole divided by x^2+1+1/x^2

=(1+1/x^2)/(x^2+1/x^2-2)+2+1

  • Here, x^2+1/x^2-2 = (x-1/x)^2

=(1+1/x^2)/(x-1/x)^2+3

So from question-

Int. (1+1/x^2) dx/(x-1/x)^2+3__________A

Taking (x-1/x)= t

Differentiating ‘x' with respect to ‘t'

1+1/x^2 dx = dt putting this value in equation no.A we get

=Int. {dt/t^2+(√3)^2}

= 1/√3 tan^-1 (t/√3)

again putting the value of ‘t'

= 1/√3 tan^-1 (x-1/x)/√3

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