Home
Class 12
MATHS
[The value of "int(sqrt(x^(2)+1){log(e)(...

[The value of "int(sqrt(x^(2)+1){log_(e)`(x^(2)+1)-2log_(e)x})/(x^(4))dx" is equal to "],[" (a) "(2)/(3)(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))-(2)/(3)}+C],[" (b) "-(1)/(3)(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))-(2)/(3)}+C],[" (c) "(1+(1)/(x^(2)))^(3/2)*{log(1+(1)/(x^(2)))+(2)/(3)}+C`]

Text Solution

AI Generated Solution

To solve the integral \[ \int \frac{\sqrt{x^2 + 1} \left( \log_e(x^2 + 1) - 2\log_e(x) \right)}{x^4} \, dx, \] we will follow these steps: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

log _(e). (1+3x)/(1-2x) is equal to

int_(1//3)^(3)(1)/(x)log_(e)(|(x+x^(2)-1)/(x-x^(2)+1)|)dx is equal to

log_(2)(x+1)-log_(2)(3x-1)=2

int(ln((x-1)/(x+1)))/(x^(2)-1)dx is equal to (a) (1)/(2)(ln((x-1)/(x+1)))^(2)+C(b)(1)/(2)(ln((x+1)/(x-1)))^(2)+C(c)(1)/(4)(ln((x-1)/(x+1)))^(2)+C(d)(1)/(4)(ln((x+1)/(x-1)))^(2)+C

The value of 1+(log_(e)x)+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+…infty

int_(1)^(3) (dx)/(x^(2)(x+1))=(2)/(3)+log .(2)/(3)

The value of x,log_((1)/(2))x>=log_((1)/(3))x is

The value of int_(1)^(e)(1+x^(2)ln x)/(x+x^(2)ln x)*dx is :

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to:

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to :