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int(x^(4)-1)/(x^(2)sqrt(x^(4)+x^(2)+1))d...

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

A

`sqrt((x^(4) + x^(2) + 1)/(x))+c`

B

`(x^(2))/( sqrt(x^(4) + x^(2) + 1))+c`

C

`x(x^(4) + x^(2) + 1)^(3//2) + c `

D

`(sqrt(x^(4) +x^(2) + 1))/( x )+c`

Text Solution

Verified by Experts

`int( x^(4) - 1)/( x^(2) (x^(4)+ x^(2) + 1)^(1//2) ) dx = int( 2x^(4) +x^(2)- ( x^(4)+x^(2) +1))/( x^(2) sqrt(x^(4) + x^(2) + 1))dx = int ((x(4x^(3) + 2x))/(2 sqrt( x^(4) +x^(2)+ 1))-sqrt(x^(4)+x^(2) + 1))/(x^(2))dx `
`=int(d)/( dx) ((sqrt(x^(4) + x^(2) +1))/( x))dx = ( sqrt( x^(4)+x^(2)+1))/(x ) + c `
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VMC MODULES ENGLISH-JEE MAIN REVISION TEST - 25 | JEE - 2020-MATHEMATICS
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  2. If f'(x)=(dx)/((1+x^(2))^(3//2)) and f(0)=0. then f(1) is equal to

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

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  5. Negation of the conditional, ..If it rains, I shall go to school.. is:

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  7. sin 12 ^(@) sin 48^(@) sin 54 ^(@) = (1)/(8).

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  8. let f(x) be a polynomial function of second degree. If f(1)=f(-1)and a...

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  9. How many numbers greater than 40000 can be formed from the digits 2,4,...

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  10. A spherical iron ball of radius 10cm, coated with a layer of ice of un...

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  11. The straight line whose sum of the intercepts on theaxes is equal to h...

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  12. If the eccentricites of the ellipse x^(2)/4+y^(2)/3=1 and the hyperbol...

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  13. The number of real root of the equal x^(3) -6x +9 = 0 is :

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  14. A person draws a card from a well shuffled pack of 52 playing cards. R...

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  15. find that the distance of the point of intersection of the line (x-2)/...

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  16. int (-pi)^(pi) (sin^(4)x)/(sin^(2) x + cos^(4) x )dx is equal to

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  17. If A=[{:(1,-1,1),(0,2,-3),(2,1,0):}] and B=(adjA) and C=5A, then find ...

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  18. The projection of the line segment joining the points ( -1,0,3) and (2...

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  19. In the expansion of ( 1 + x+ x^(2) + x^(3))^(6) , the coefficient of x...

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  20. if ( dy )/(dx) =1 + x +y +xy and y ( -1) =0 , then the value of ( y (...

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