Home
Class 12
MATHS
Integrate the functionssqrt(x^2+4x+6)...

Integrate the functions`sqrt(x^2+4x+6)`

Text Solution

Verified by Experts

`x^2+4x+6=(x+2)^2+2=(x+2)^2+(sqrt2)^2`
Let `x+2=t=>dx=dt`
Also we know that, `intsqrt(a^2+x^2)dx=x/2sqrt(a^2+x^2)+a^2/2log|x+sqrt(x^2+a^2)|+c`
`:. int sqrt(x^2+4x+6)dx=intsqrt(((x+2)^2)+(sqrt2)^2)dx`
...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.5|23 Videos

  • INTEGRALS

    NCERT|Exercise MISCELLANEOUS EXERCISE|44 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.10|10 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

Integrate the functions sqrt(x^(2)+3x)

Integrate the functions x sqrt(x+2)

Integrate the functions sqrt(x^(2)+4x+1)

Integrate the functions sqrt(x^(2)+4x-5)

Integrate the functions sqrt(1-4x^(2))

Integrate the functions sqrt(4-x^(2))

Integrate the functions sqrt(1-4x-x^(2))

Integrate the functions (1)/(sqrt(x^(2)+2x+2))

Integrate the functions sqrt(1+3x-x^(2))

Integrate the functions sin^(4)x

Home
Profile