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

Evaluate `int(dx)/(x-sqrt(x^(2)+2x+4))`.

Text Solution

Verified by Experts

The correct Answer is:

`2ln|sqrt(x^(2)+2x+4)-x|-(3log)/(2 (sqrt(x^(2)+2x+4)-(x+1)))-3/2lnsqrt(x^(2)+2x+4-x-1)+C`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

INDEFINITE INTEGRAL
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos
INDEFINITE INTEGRAL
ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|9 Videos
HYPERBOLA
ARIHANT MATHS|Exercise Hyperbola Exercise 11 : Questions Asked in Previous 13 Years Exams|3 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

ARIHANT MATHS-INDEFINITE INTEGRAL -Exercise (Subjective Type Questions)

The value of int e^((x sin x+ cos x)).((x^(4)cos^(3)x-x sin x + cos...
Text Solution
|
Evaluate : intsqrt(x+sqrt(x^(2)+2))dx
Text Solution
|
Evaluate int (dx)/((sqrt((x-alpha)^(2)-beta^(2)))(ax+b)).
Text Solution
|
Evaluate int(sqrt(1+root(3)(x)))/(root(3)(x^(2)))dx.
Text Solution
|
Evaluate: intsin^3(theta/2)/(cos(theta/2)sqrt(cos^3theta+cos^2theta+co...
Text Solution
|
Find the discriminant of the following quadratic equation : 2x^2 -2√...
Text Solution
|
Find the discriminant of the following quadratic equation : 3x^2 + 2...
Text Solution
|
Find the discriminant of the following quadratic equation : 2x^2 + 5...
Text Solution
|
Evaluate int(dx)/((sinx+a s e c x)^2) when |a|> 1/2.
Text Solution
|
Evaluate int(dx)/(x-sqrt(x^(2)+2x+4)).
Text Solution
|
Evaluate int(dx)/(sqrt(x^(2)+2x+2)).
Text Solution
|
Evaluate: int(x^4+1)/(x^6+1)dx
Text Solution
|
Evaluate int(dx)/(x^3-1)
Text Solution
|
Evaluate: int([sqrt(1+x^2)+x]^n)/(sqrt(1+x^2))dx
Text Solution
|
If y^(2)=ax^(2)+2bx+c and u(n)= int (x^(n))/(y)dx, prove that (n+1)a u...
Text Solution
|