Home
Class 12
MATHS
Evaluate: int1/(sqrt(3x+4)-sqrt(3x+1))dx...

Evaluate: `int1/(sqrt(3x+4)-sqrt(3x+1))dxdot`

Text Solution

Verified by Experts

`int1/(sqrt(3x+4)-sqrt(3x+1))dx`

Multiplying by its conjugate

`=int(sqrt(3x+4)+sqrt(3x+1))/((sqrt(3x+4)-sqrt(3x+1))(sqrt(3x+4)-sqrt(3x+1)))dx`

`=int(sqrt(3x+4)+sqrt(3x+1))/((3x+4)-(3x+1))dx`

`=int(sqrt(3x+4)+sqrt(3x+1))/(3)dx`

`=(2(3x+4)^(3/2)+2(3x+1)^(3/2))/(27)+C`

Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(1)/(sqrt(3x+4)-sqrt(3x+1))dx

Evaluate: (i)int(1)/(sqrt(3x+4)-sqrt(3x+1))dx

int(1)/(sqrt(3x+2)+sqrt(3x+1))

int(1)/(sqrt(1+x)+sqrt(x+3))dx

int1/sqrt(5-3x)dx

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

int(dx)/((sqrt(1-3x)-sqrt(5-3x)))

Evaluate: int1/(sqrt(8+3x-x^2))\ dx

Evaluate : int 1 /( sqrt( x + 3 ) - sqrt( x + 2 ) ) dx

Evaluate: int1/(sqrt(7-3x-2x^2))\ dx