Evaluate the following integral: int0^1(...

Evaluate the following integral: `int_0^1(sqrt(tan^(-1)x))/(1+x^2)dx`

Text Solution

AI Generated Solution

To evaluate the integral \[ I = \int_0^1 \frac{\sqrt{\tan^{-1} x}}{1+x^2} \, dx, \] we will use the substitution \( t = \tan^{-1} x \). ...

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

CONTINUITY
RD SHARMA|Exercise Solved Examples And Exercises|277 Videos
DERIVATIVES AS A RATE MEASURER
RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following integral: int_0^1(tan^(-1)x)/(1+x^2)dx

Evaluate the following integral: int_0^1tan^(-1)x\ dx

Evaluate the following integral: int_0^1tan^(-1)\ ((2x)/(1-x^2))dx

Evaluate the following integral: int_0^1tan^(-1)((2x)/(1-x^2))dx

Evaluate the following integral: int_1^5x/(sqrt(2x-1))dx

Evaluate the following integral: int_0^a1/(x+sqrt(a^2-x^2))dx

Evaluate the following : int_(0)^(1)(sqrt(tan^(-1)x))/(1+x^(2))dx.

Evaluate the following integral: int_0^4|x-1|dx

Evaluate the following integrals: inte^(x)(tan^(-1)x+(1)/(1+x^(2)))dx

Evaluate the following integrals: int(x^(2)tan^(-1)x)/((1+x^(2)))dx

RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises

Evaluate the following integral: int0^(pi//2)sqrt(sinvarphi)cos^5varph...
05:12
|
Evaluate the following integral: int0^(pi//2)(sintheta)/(sqrt(1+costhe...
04:01
|
Evaluate the following integral: int0^1(sqrt(tan^(-1)x))/(1+x^2)dx
02:12
|
Evaluate the following integral: int0^1tan^(-1)\ ((2x)/(1-x^2))dx
03:23
|
Evaluate the following integral: int0^(pi//2)(dx)/(acosx+bsinx)x
06:24
|
Evaluate the following integral: int0^pi(sinx)/(sinx+cosx)dx
03:42
|
Evaluate the following integral: int0^1tan^(-1)x\ dx
01:08
|
Evaluate the following integral: int0^(pi//4)(sqrt(t a n x)+sqrt(cotx)...
05:21
|
Evaluate the following integral: int0^pi1/(5+3cosx)dx
02:19
|
Evaluate the following integral: int0^(pi//2)(x+sinx)/(1+cosx)dx
03:07
|
Evaluate the following integral: int0^(pi//4)(sin x+cosx)/(3+sin2x)dx
06:07
|
Evaluate the following integral: int0^1(1+x^2)/(x^4+x^2+1)dx
04:15
|
Evaluate the following integral: int4^(12)x(x-4)^(1//3)dx
02:02
|
Evaluate the following integral: int(-1)^1 5x^4sqrt(x^5+1)dx\
01:36
|
Evaluate the following integral: int0^(pi//4)sin^3 2tcos2t\ dt
01:09
|
Evaluate the following integral: int0^(pi//2)(cos x)/(1+sin^2x)dx
01:03
|
Evaluate the following integral: int0^(pi//3)(cos\ x)/(3+4sinx)dx
01:47
|
Evaluate the following integral: int0^2x\ sqrt(x+2)\ dx
02:57
|
Evaluate the following integral: int0^(pi//2)(sinxcosx)/(1+sin^4x)dx
01:08
|
Evaluate the following integral: int0^pi1/(5+4sinx)dx
03:48
|