Evaluate int0^1 (loge (1+x))/(1+x^2)dx...

Evaluate `int_0^1 (log_e (1+x))/(1+x^2)dx`

Text Solution

Verified by Experts

The correct Answer is:

`pi/8 ln 2`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

INTEGRATION
ARIHANT PRAKASHAN|Exercise TOPIC TEST 2|19 Videos
INTEGRATION
ARIHANT PRAKASHAN|Exercise CHAPTER TEST (1 MARK QUESTIONS) |10 Videos
INTEGRATION
ARIHANT PRAKASHAN|Exercise TOPIC 2 (PRACTISE QUESTIONS) (4 MARK QUESTIONS)|28 Videos
EXAMINATION PAPER 2019
ARIHANT PRAKASHAN|Exercise Group -C|11 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
ARIHANT PRAKASHAN|Exercise Chapter Test (6 MARKS Questions) |3 Videos

ARIHANT PRAKASHAN-INTEGRATION -TOPIC 2 (PRACTISE QUESTIONS) (6 MARK QUESTIONS)

Evaluate int0^ pi x/(1+ sin x) dx
Text Solution
|
Evaluate int0^1 (loge (1+x))/(1+x^2)dx
Text Solution
|
Prove that int0^(pi//4) cos^2 2x sin^3 4x dx=1/6
Text Solution
|
Evaluate int0^(pi//2) (sin x(7- cos x))/((1+cos ^2 x) (2- cos x)) dx
Text Solution
|
Evaluate int0^(pi//2) ((1-sin^2 x) (4 sin x-3))/((4- cos^2 x) (sin x+4...
Text Solution
|
Evaluate int0^(pi//2) (dx)/(1+2cos x)
Text Solution
|
Find int1^2 x dx as a limit of sum.
Text Solution
|
Evaluate int0^(-pi//2) sin x dx
Text Solution
|
Evaluate int0^(pi//2) (cosx)/ (cos^2x+ sin^2 x) dx
Text Solution
|
Evaluate int(pi//2)^ pi e^x ((1- sin x)/(1- cos x))dx
Text Solution
|