Home
Class 12
MATHS
Integrate the functions1/(x-x^3)...

Integrate the functions`1/(x-x^3)`

Text Solution

Verified by Experts

`int (1)/(x-x^(3)) dx= int(1)/(x(1-x^(2)))dx`
`=int (1)/(x(1-x)(1+x))dx" "......(1)`
` " Let " (1)/(x(1-x)(1+x)) =(A)/(x)+(B)/((1-x))+(C)/((1-x))`
`rArr 1=A(1+x)(1-x)+B(x)(1+x)+C(x)(1-x)`
`x=-1 " then " 1=0 +0+ C(-1)(2)rArr B=(1)/(2)`
`x=1 " then " 1=A (1) (1)+0 +0 rArr A=1`
`:. int (1)/(x(1-x^(2)))dx`
`=int(1)/(x) dx+ (1)/(2) int (1)/(1-x)dx-(1)/(2) int (1)/(1+x) dx`
`=log |x| -(1)/(2) log |1-x| -(1)/(2) log |1+x|+C`
`=(1)/(2) log |(x^(2))/(1-x^(2))|+C`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.11|21 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

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

Similar Questions

Explore conceptually related problems

Integrate the functions 1/(x^2(x^4+1)^(3/4))

Integrate the functions 1/(x^(1/2)+x^(1/3)) [Hint: 1/(x^(1/2)+x^(1/3))=1/(x^(1/3)(1+x^(1/6)) , put x = t^6 ]

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

Integrate the functions 1/(x(logx)^m), x >0

Integrate the functions xsin3x

Integrate the functions ((x-3)e^x)/((x-1)^3)

Integrate the functions (x^3-1)^(1/3)x^5

Integrate the functions (x^3-1)^(1/3)x^5

Integrate the functions (x^3)/(sqrt(1-x^8)) dx

Integrate the functions 1/(x-sqrt(x))

Home
Profile