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int(x^(2)+1)/(x^(4)-x^(2)+1)dx= . . ....

`int(x^(2)+1)/(x^(4)-x^(2)+1)dx=` . . .

A

`tan^(-1)((x^(2)+1)/(2))+c`

B

`tan^(-1)(x^(2))+c`

C

`tan^(-1)(2x^(2)-1)+c`

D

`tan^(-1)((x^(2)-1)/(x))+c`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l=int(x^(2)+1)/(x^(4)-x^(2)+1)dx=int(1+(1)/(x^(2)))/(x^(2)-1+(1)/(x^(2)))dx=int(1+(1)/(x^(2)))/((x-(1)/(x))^(2)+1)`
put `x-(1)/(x)=t`
`(1+(1)/(x^(2)))dx=dt`
`thereforel=int(dt)/(t^(2)+1)=tan^(-1)(t)+c`
`=tan^(-1)(x-(1)/(x))+c=tan^(-1)((x^(2)-1)/(x))+c`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-SOLVED PAPER 2019-MCQS
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  6. Which of the following statements is contingency?

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  7. int(a)^(b)(sqrt(x))/(sqrt(x)+sqrt(a+b-x))dx=. . . .

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  8. The intercept on line y = x by circle x^2 + y^2- 2x = 0 is AB. Find eq...

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  11. If 4sin^(-1)x+6cos^(-1)x=3pi then x= . . .

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  12. If int(0)^(a)sqrt((a-x)/(x))dx=(K)/(2), then K=. . .

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  13. In DeltaABC, with usual notations, (bsinB-c sin C)/(sin(B-C))=. . . .

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  14. The solution of the differential equation (d theta)/(dt)=-k(theta-thet...

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  15. The vector equation of the plane r=(2hati+hatk)+lamda(hati)+mu(hati+2h...

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  16. Area of the region bounded by y=cosx,x=0,x=pi and X-axis is . . .sq....

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  17. The length of the latusrectum of an ellipse is (18)/(5) and eccentrici...

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  18. Let a:~(p ^^ ~r) vv (~ q vv s ) and b:(p vv s ) lar (q ^^ r). If the t...

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  19. "If two triangles are congruent, then their areas are equal" is the gi...

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