Home
Class 12
MATHS
int(2x)/(x^2+3x+2)dx...

`int(2x)/(x^2+3x+2)dx`

Text Solution

Verified by Experts

` (2x)/(x^(2)+3x+2)=(2x)/(x^(2)+2x+x+2)`
` =(2x)/(x(x+2)+1(x+2))`
`=(2x)/((x+2)(x+1))`
`" Let " (2x)/((x+2)(x+1)) =(A)/((x+2)) +(B)/((x+1))`
` rArr (2x)/((x+2)(x+1))=(A(x+1)+B(x+2))/((x+2)(x+1))`
`rArr 2x=A (x+1)+B(x+2)`
` x=-1 " then " -2 =0 +B (1) rArr B=-2`
`x=-2 " then " -4 =A(-1)+0 rArr A=4`
`:. int(2x)/((x+2)(x+1))dx`
` = int(A)/((x+2))dx +int(B)/((x+1))dx`
`=int(4)/((x+2))dx + int ((-2))/((x+1))dx`
`=4 log |x+2|-2log |x+1|+c`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7.6|24 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7.7|11 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Exercise 7.4|25 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

int(x)/(x^(2)+3x+2)dx

Evaluate: int(x)/(x^(2)+3x+2)dx

1. int(x)/(x^(2)+3x+2)dx

" 1."int(x)/(x^(2)+3x+2)dx

int(x)/(x^(2)-3x+2)*dx

int(2x-3)/(x^(2)-3x+2)dx

Evaluate : int(2x+3)/(x^(2)+3x+2)dx .

int(x-2)/(x^(2)-3x+2)dx

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

int(5x-1)/(3x^2+x+2)dx=