Home
Class 12
MATHS
Evaluate: int(x^2+1)/(x^4+1)dx...

Evaluate: `int(x^2+1)/(x^4+1)dx`

Text Solution

Verified by Experts

`I=int(x^(2)+1)/(x^(4)+1)dx = int(1+(1)/(x^(2)))/(x^(2)+(1)/(x^(2)))dx=int(1+(1)/(x^(2)))/((x-(1)/(x))^(2)+2)dx`
Let `x-(1)/(x)=t " or " d(x-(1)/(x))=dt " or " (1+(1)/(x^(2)))dx=dt`
`:. I=int(dt)/(t^(2)+(sqrt(2))^(2))=(1)/(sqrt(2))tan^(-1)((t)/(sqrt(2)))+C`
`=(1)/(sqrt(2))tan^(-1)((x-1//x)/(sqrt(2)))+C`
`=(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2)x))+C`
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate: int((1+x^2)/(x^4))dx

Evaluate: int(x^4+1)/(x^6+1)dx

Evaluate: int(x^2+1)/(x(x^2-1))dx

Evaluate: int((x^2+1))/(x^4-x^2+1)\ dx

Evaluate: int1/(x^4-1)dx

Evaluate: int1/(x^4+1)dx

Evaluate: int(x^2-1)/((x^2+1)sqrt(x^4+1))dx

Evaluate: int(x^2-1)/((x^4+3x^2+1)tan^(-1)(x+1/x))dx

Evaluate int(1)/(x^(2)+4x+10)dx

Evaluate int (x-1)/(x^2-2x+1)dx