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sir / mam solve this question take refrence from image i have uploaded

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6 months ago

2065 Points
```							we wish to integrate (1+x^2)/(4x^4 – 4sqrt2*x + 3)note that 4x^4 – 4sqrt2*x + 3= (2x^2+2sqrt2x+3)(2x^2 – 2sqrt2x+1)once we see this factorisation, the ques becomes easy.also, note that the sum of factors 2x^2+2sqrt2x+3 and 2x^2 – 2sqrt2x+1 is 4(x^2+1)hence, (1+x^2)/(4x^4 – 4sqrt2*x + 3)= [1/(2x^2+2sqrt2x+3) + 1/(2x^2 – 2sqrt2x+1)]/4= [1/(4x^2+4sqrt2x+6) + 1/(4x^2 – 4sqrt2x+2)]/2now write 4x^2 – 4sqrt2x+2= (2x – sqrt2)^2and 4x^2+4sqrt2x+6= (2x+sqrt2)^2 + (2)^2after that the integration of these 2 quantities becomes extremely easy since they turn into std forms.KINDLY APPROVE :))
```
5 months ago
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### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions