Home
Class 12
MATHS
For real numbers alpha, beta, gamma and ...

For real numbers `alpha, beta, gamma and delta` , if
`int((x^(2)-1)+tan^(-1)((x^(2)+1)/(x)))/((x^(4)+3x^(2)+1)tan^(-1)((x^(2)+1)/(x)))dx`
`= alpha log_(e)(tan^(-1)((x^(2)+1)/(x)))+beta "tan"^(-1)((gamma(x^(2)-1))/(x))+delta tan ((x^(2)+1)/(x))+C`
where is an arbitrary constant, then the value of `10(alpha+betagamma+delta)` is equal to........

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematic section A|20 Videos
  • JEE MAIN

    JEE MAINS PREVIOUS YEAR|Exercise QUESTION|1 Videos
  • JEE MAIN 2022

    JEE MAINS PREVIOUS YEAR|Exercise Question|454 Videos

Similar Questions

Explore conceptually related problems

If int((x^(2)-1)dx)/((x^(4)+3x^(2)+1)Tan^(-1)((x^(2)+1)/(x)))=klog|tan^(-1)""(x^(2)+1)/x|+c , then k is equal to

int(2x+3)/((x-1)(x^(2)+1))dx=log_(e){(x-1)^((5)/(2))(x^(2)+1)^(a)-(1)/(2)tan^(-1)x+C,x>1 where C is any arbitrary constant,then the value of a'a' is

The value of int_(0)^(1)(tan^(-1)((x)/(x+1)))/(0tan^(-1)((1+2x-2x^(2))/(2)))dx is

The value of int_(0)^(1)(tan^(-1)((x)/(x+1)))/(0tan^(-1)((1+2x-2x^(2))/(2)))dx is

Let int_(0)^(1)tan^(-1)((tan x)/(2))dx=alpha then int_(0)^(1)tan^(-1)((tan x-2cot x)/(3))dx is

(i) int(1)/((1+x^(2))tan ^(-1) x )dx " "(ii) int(e^(tan^(-1)x))/(1+x^(2))dx

If int(sin x)/(sin^(3)x + cos^(3)x) dx = alpha log_(e)|1 + tan x| + beta log_(e)|1-tan x + tan^(2)x| + gamma tan^(-1)((2 tan x - 1)/(sqrt(3))) + C , when C is constant of integration, then the value of 18(alpha+ beta + gamma^(2)) is __________.

The value of int(e^(x)(x^(2)tan^(-1)x+tan^(-1)x+1))/(x^(2)+1)dx is equal to

int(dx)/(x^(2)+2x+2) equals (A) x tan^(-1)(x+1)+C (B) tan^(-1)(x+1)+C