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

The integral `int (2x-3)/(x^2+x+1)^2 .dx` is equal to

A

`-(8x+7)/(x^(2)+x+1)-(16)/(3sqrt(3))tan^(-1)((2x+1)/(3))+C`

B

`-(1)/(x^(2)+x+1)-(4)/(3)tan^(-1)(4x+3)+C`

C

`(1)/(2(x^(2)+x+1))-((2x+1)^(2))/((x^(2)+x+1)^(2))+C`

D

`(1)/(4(x^(2)+x+1))+(2)/(3)tan^(-1)(2x+1)+C`

Text Solution

Verified by Experts

The correct Answer is:

a

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

INDEFINITE INTEGRALS
OBJECTIVE RD SHARMA|Exercise Exercise|62 Videos
INCREASING AND DECREASING FUNCTIONS
OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos
INTEGRALS
OBJECTIVE RD SHARMA|Exercise Illustration|1 Videos

Similar Questions

Explore conceptually related problems

The integral int((x)/(x sin x+cos x))^(2)dx is equal to (where "C" is a constant of integration

The integral int((x)/(x sin x+cos x))^(2)" dx is equal to (where C is a constant of integration )

Knowledge Check

The integral int(2x^(3)-1)/(x^(4)+x)dx is equal to: (Here C is a constant of integration)

A

`(1)/(2) log_(e).(|x^(3)+1|)/(x^(2))+C`

B

`(1)/(2)log_(e).(x^(3)+1)^(2)/|x^(3)|+C`

C

`log_(e)|(x^(3)+1)/(x)|+C`

D

`log|x^(3)+1|/(x^(2))+C`

The integral int(2x^(3)-1)/(x^(4)+x)dx is equal to (here C is a constant of intergration)

A

`(1)/(2)"log"_(e)(|x^(3)+1|)/(x^(2))+C`

B

`(1)/(2)"log"_(e)(|x^(3)+1|^(2))/(|x^(3)|)+C`

C

`"log"_(e)|(x^(3)+1)/(x)|+C`

D

`"log"_(e)(|x^(3)+1|)/(x^(2))+C`

The integral int(2)/(e^(2x)-1)dx is equal to (Here C is a constant of integration)

A

`x+log_(e)|e^(x)+e^(-x)|+C`

B

`-x+log_(e)|e^(x)-e^(-x)|+C`

C

`-x+log_(e)|e^(x)+e^(-x)|+C`

D

`x+log_(e)|e^(x)-e^(-x)|+C`

Similar Questions

Explore conceptually related problems

The integral int_(0)^(pi/2)(dx)/(1+cos x) is equal to

The value of the integral int(dx)/(x(1+logx)^2) is equal to

The integral int_(-1)^(2) (|x+2|)/(x+2)dx is equal to

The integral int_(-1)^(1) (|x+2|)/(x+2)dx is equal to

int(2x^(3)-1)/(x^(4)+x)dx is equal to

OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Chapter Test

The integral int (2x-3)/(x^2+x+1)^2 .dx is equal to
12:01
|
If int (xtan^(-1)x)/sqrt(1+x^2) dx = sqrt(1+x^2)f(x)+Aln|x+sqrt(x^2+1)...
02:47
|
Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...
05:04
|
If int(xe^x)/sqrt(1+e^x)dx=f(x)sqrt(1+e^x)-2logg(x)+c, then
08:20
|
The value of the integral int (cos^3x+cos^5 x)/(sin^2 x+sin^4 x) dx is...
06:26
|
If int(1)/((x^(2)+1)(x^(2)+4))dx=Atan^(-1)x+B" tan"^(-1)(x)/(2)+C , t...
03:44
|
If int log(sqrt(1-x)+sqrt(1+x))dx=xf(x)+Ax+Bsin^(-1)x+C, then
06:27
|
If int(x^(5))/(sqrt(1+x^(3)))dx is equal to
02:41
|
The value of inte^(secx)*sec^3x(sin^2x+cosx+sinx+sinxcosx)dx is
06:53
|
int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=alog((x+1)/(x-1))+b"tan"^(-1)(x)/...
05:45
|
Let f(x)=x/((1+x^n)^(1/ n)) for ngeq2 and g(x)=(f(ofo ...of)(x) Then ...
04:31
|
The value of int((ax^2-b)dx)/(xsqrt(c^2x^2-(ax^2+b)^2)) is equal to
02:26
|
Evaluate: inte^x(1+n x^(n-1)-x^(2n))/((1-x^n)sqrt(1-x^(2n)))dx
05:26
|
int(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx
06:48
|
int(x^(3))/((1+x^(2))^(1//3))dx is equal to
03:09
|
int sinx/sin(x-alpha)dx=Ax+B log (sin(x-alpha))+C then find out A & B
03:25
|
What is int (x^(4) -1)/(x^(2) sqrt(x^(4) + x^(2) + 1)) dx equal to ?
07:34
|
int(x-1)/((x+1)sqrt(x^(3)+x^(2)+x))dx is equal to
02:27
|
int(1+x^(2))/(xsqrt(1+x^(4)))dx is equal to
03:49
|
int(1+x^(4))/((1-x^(4))^(3//2))dx is equal to
02:02
|