Evaluate int(2)^(3)(2x^(5)+x^(4)-2x^(3)+...

Evaluate `int_(2)^(3)(2x^(5)+x^(4)-2x^(3)+2x^(2)+1)/((x^(2)+1)(x^(4)-1))dx`

Text Solution

Verified by Experts

The correct Answer is:

`[(1)/(2)(log 6-(1)/(5))]`

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

DEFINITE INTEGRALS
AAKASH SERIES|Exercise Exercise - 2.7 (Level-2)|21 Videos
COMPLEX NUMBERS
AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos
DEMOIVRE'S THEOREM
AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

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

Evaluate int(x^(2))/(x^(4)+x^(2)+1)dx

Knowledge Check

int_(-1)^(1) (17x^(5)-x^(4)+29 x^(3) -31 x +1)/(x^(2)+1)dx=

A

`4/5`

B

`5/4`

C

`4/3`

D

`3/4`

int (1)/((x^(2) + 1)(x^(2)+ 4)) dx =

A

`(1)/(3) [ tan^(-1) x - (1)/(2) tan^(-1)""(x)/(2)] + c`

B

`(1)/(3) [ tan^(-1) x + (1)/(2) tan^(-1)""(x)/(2)] + c`

C

`(1)/(3) [tan^(-1) x - (x)/(2) + 2 tan^(-1) x] + c`

D

`(2)/(3) [ tan^(-1) x - (3)/(2) tan^(-1)""(x)/(2)] + c`

Similar Questions

Explore conceptually related problems

Evaluate int(x^(2))/(x^(4)-x^(2)+1)dx

int_(2)^(3) (2x)(1+x^2) dx

Evaluate int_(1)^(2)((x+1)^(3))/(x^(2))dx

Evaluate int_(1)^(2) ((x+1)^(3))/(x^(2)) dx

Evaluate int_(1)^(4) x sqrt(x^(2)-1) dx

Evaluate int(1)/(x^(4)-x^(2)+1)dx

AAKASH SERIES-DEFINITE INTEGRALS-Exercise (Level-2)

Evaluate int(2)^(3)(2x^(5)+x^(4)-2x^(3)+2x^(2)+1)/((x^(2)+1)(x^(4)-1))...
11:43
|
Show that int(0)^(pi//4)(x^(2))/((x sin x + cos x)^(2))dx - (4-pi)/(4+...
11:57
|
Show that int(1)^(2)(x+(1)/(x))^(3//2)((x^(2)-1)/(x^(2)))dx = ((5)/(2)...
06:10
|
Show that int(2)^(2sqrt(3)) x^(3)(x^(2)-3)^(3//2)dx = (16012)/(35)
05:21
|
Prove that int(0)^(oo) (dx)/((x^(2)+a^(2))(x^(2)+b^(2)))=(pi)/(2ab(a+b...
06:16
|
Prove that int(a)^(oo) (dx)/(x^(4)sqrt(a^(2) + x^(2)))=(2-sqrt(2))/(3a...
07:32
|
Prove that int(0)^(pi//2) "cosec" (x-(pi)/(3))"cosec"(x-(pi)/(6)) dx =...
06:47
|
Show that int(0)^(oo) (dx)/([x+sqrt(x^(2)+1)]^(3)) = (3)/(8)
07:06
|
Show that int(0)^(pi)cos (2 cot^(-1) (sqrt((1-x)/(1+x))))dx = -(1)/(2)
05:40
|
Show that int(0)^(pi//2) (dx)/(3+4 six) = (1)/(sqrt(7)) log((4+sqrt(7)...
13:52
|
If int(log 2)^(x) (dy)/(sqrt(e^(y) -1)) = (pi)/(6), prove that x = log...
05:40
|
If int(log 2)^(x)(1)/(e^(x)-1)dx = log""(3)/(2), show that x = log 4
05:51
|
Show that int(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx = (1)/(2)-(sqrt...
07:12
|
Prove that int(0)^(pi//2) tan^(-1)(sin x) .sin 2x = (pi)/(2)-1
08:27
|
Show that (a) int(e)^(e^(2))(1)/(log x)dx = int(1)^(2)(e^(x))/(x)dx ...
05:19
|
Prove that int(0)^(1) log(sqrt(1-x)+sqrt(1+x))dx = (1)/(2) log 2 + (pi...
12:39
|
Show that int(0)^(pi//4) x cos x cos 3 x dx = (pi-3)/(16)
07:49
|
Prove that int(0)^(oo) e^(-2x)(sin 2x + cos 2 x) dx = (1)/(2)
09:32
|
Show that int(0)^(pi//2) (cos x)/((1+sin x)(2+sin x)) dx = log((4)/(3...
05:08
|
Show that int(1)^(7thsqrt(2))(1)/(x(2x^(7) + 1))dx=(1)/(7) log((6)/(5)...
06:15
|