Home
Class 12
MATHS
int (3x-1)/(x-2)^2 dx...

`int (3x-1)/(x-2)^2 dx`

Text Solution

Verified by Experts

`" Let " (3x-1)/((x+2)^(2))=(A)/((x+2))+(B)/((x+2)^(2))`
`rArr (3x-1)/((x+2)^(2))=(A(x+2)+B)/((x+2)^(2))`
`rArr 3x-1 =A(x+2) +B`
`x=-2 " then " -6 -1 =0 +B rArr B=-7`
Equating the coefficients of x,
`3=A`
`:. (3x-1)/((x+2)^(2)) =(3)/((x+2)) -(7)/((x+2)^(2))`
`rArr int (3x-1)/((x+2)^(2))dx`
`= 3 int (1)/((x+2))dx-7 int(1)/((x+2)^(2))dx`
`=3 log |x+2|-7 ((-7)/(x+2))+c`
`=3 log |x+2| +(7)/(x+2)+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(3x+1)/((x-2)^2(x+2))dx

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

int(x^(2))/(sqrt(3x+4))dx (ii) int(2x-1)/((x-1)^(2))dx

int (x^2-1)(x^3-3x)^2 dx

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

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

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

Column I a) int(x^2-x+1)/(x^3-4x^2+4x)dx b) int(x^2-1)/(x(x-2)^3)dx c) int(x^3+1)/(x(x-2)^2)dx d) int(x^5+1)/(x(x-2)^3)dx COLUMN II (which of the following functions appear in integration of functions in columnI) p) log|x| q) log|x-2| r.) 1/((x-2)) s) x

int (dx)/((x+1)(2x+1)) (ii) int (x-1)/((x-2)(x-3)) dx .

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