Integrate the functionsxsqrt(1+2x^2)...

Integrate the functions`xsqrt(1+2x^2)`

Text Solution

AI Generated Solution

To solve the integral of the function \( x \sqrt{1 + 2x^2} \), we will use the substitution method. Here’s a step-by-step solution: ### Step 1: Choose a substitution Let: \[ t = 1 + 2x^2 \] Then, we need to differentiate \( t \) with respect to \( x \): ...

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

INTEGRALS
NCERT ENGLISH|Exercise EXERCISE 7.4|25 Videos
INTEGRALS
NCERT ENGLISH|Exercise EXERCISE 7.8|6 Videos
DIFFERENTIAL EQUATIONS
NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
NCERT ENGLISH|Exercise Solved Examples|13 Videos

Similar Questions

Explore conceptually related problems

Integrate the functions sqrt(1-4x^2)

Integrate the functions xsqrt(x+2)

Integrate the functions sqrt(1+(x^2)/9)

Integrate the functions sqrt(1+(x^2)/9)

Integrate the functions sqrt(1-4x-x^2)

Integrate the functions sqrt(1+3x-x^2)

Integrate the functions sqrt(x^2+3x)

Integrate the functions (4x+2)sqrt(x^2+x+1)

Integrate the functions (4x+2)sqrt(x^2+x+1)

Integrate the functions (sqrt(x^2+1)[log(x^2+1)-2logx])/(x^4)

NCERT ENGLISH-INTEGRALS-EXERCISE 7.2

Integrate the functionssinxsin(cosx)
02:09
|
Integrate the functions sin(a x+b)cos(a x+b)
02:23
|
Integrate the functionsxsqrt(1+2x^2)
02:56
|
Integrate the functions(4x+2)sqrt(x^2+x+1)
03:12
|
int(dx)/(sin^2xcos^2x)equals(A) tanx+cotx+C (B) tanx-cotx+C(C) tanxco...
02:58
|
int(10 x^9+10 x^x(log)(e^(10))dx)/(x^(10)+10^x)equals(A) 10^x-x^(10)+C...
03:42
|
Integrate the functions(x^3sin(tan^(-1)x^4)/(1+x^8)
03:29
|
Integrate the functions((1+x)(x+logx)^2)/x
02:48
|
Integrate the functions((1+logx)^2)/x
02:34
|
Integrate the functions(sqrt(tanx))/(sinxcosx)
04:03
|
Integrate the functions1/(1-tanx)
06:12
|
Integrate the functions1/(1+cotx)
05:04
|
Integrate the functions(sinx)/((1+cosx)^2)
02:51
|
Integrate the functions(sinx)/(1+cosx)
02:01
|
Integrate the functions(cosx)/(sqrt(1+sinx))
02:31
|
Integrate the functionscotxlogsinx
02:05
|
Integrate the functions(e^(2x)-e^(-2x))/(e^(2x)+e^(-2x))
02:38
|
Integrate the functionstan^2(2x-3)
02:43
|
Integrate the functionssec^2(7-4x)
02:18
|
Integrate the functions(1.)(sec)^2(7-4x)(2.) sin^(-1)x/sqrt(1-x^2)
01:48
|