Home
Class 12
MATHS
Evaluate the following Integrals : i...

Evaluate the following Integrals :
`int(x^(4)-1)/(x^(2)(x^(4)+x^(2)+1)^(1//2))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

The correct Answer is:
D
`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))/(2sqrt(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`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 13

    VMC MODULES ENGLISH|Exercise MATHEMATICS( SECTION-2)|5 Videos

  • MOCK TEST 12

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 2

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION - 2)|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following Integrals : int(tan^(-1)x)/(x^(2))dx

Evaluate the following integral : int(1)/(x^(4)+1)dx

Evaluate the following Integrals : int (x^(2))/((x-1)(x-2)(x-3))dx

Evaluate the following integration int(x^(4))/(1+x^(2))dx

Evaluate the following integrals : int((x^3+8)(x-1))/(x^2-2x+4)dx

Evaluate the following Integrals. int (x+1)/(x^(2) + 2x +1)dx

Evaluate the following integral: int_1^3|x^2-4|dx

Evaluate the following integral: int_2^4x/(x^2+1)dx

Evaluate the following integrals : int1/(1+cos2x)dx

Evaluate the following integrals : int_1^4(3x^2+2x)dx