Home
Class 12
MATHS
Evaluate: int(3x-2)\ sqrt(x^2+x+1)\ dx...

Evaluate: `int(3x-2)\ sqrt(x^2+x+1)\ dx`

Text Solution

Verified by Experts

Let `I=int(3 x-2) sqrt{x^{2}+x+1} d x`
`Rightarrow 3 x-2=A(2 x+1)+B `
`Rightarrow 3 x-2=2 A x+(A+B)`
Equating
`2 A=3 and A+B=-2`
`A=frac{3}{2} text { and } B=-2-frac{3}{2}=-frac{7}{2}`
`I=int{frac{3}{2}(2 x+1)-frac{7}{2}}`
`sqrt{x^{2}+x+1} {dx} `
...
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(7x-2)sqrt(3x+2)dx

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

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

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

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

Evaluate: int1/(x^(3)sqrt(x^2-1))\ dx

Evaluate: int(3x-1)/sqrt (3x^2-2x+7)dx

Evaluate: (i) int(4x+2)sqrt(x^(2)+x+1)dx (ii) int(4x+3)/(sqrt(2x^(2)+3x+1))dx

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

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