Home
Class 12
MATHS
Let f ((x + 1 ) /( x - 1 )) = 2x + 1...

Let ` f ((x + 1 ) /( x - 1 )) = 2x + 1 `, then integral ` int f (x ) dx ` is ` (x ne 1 )`.

A

` x ^ 2 + x + c `

B

` 2 x + ln | x + 1 | + c `

C

` 3x + 4ln | x - 1 | + c `

D

`2 x + 3 ln | x + 1 | + c `

Text Solution

Verified by Experts

The correct Answer is:
C
`f((X + 1)/(x-1)) = 2x + 1`
Put `(x + 1)/(x-1) = t `
` rArr " " x = (t +1)/(t -1)`
`rArr " " f(x) = (3x +1)/(x-1) " "int(3x +1)/(x-1) dx = int (3 + (4)/(x-1))dx`
` = x + 3 In |x -1| + C`
` int f(x) dx = 3x + 4 In | x -1 | + C`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)=log_(e)|x-1|, x ne 1 , then the value of f'((1)/(2)) is

If 2f(x) - 3 f(1//x) = x," then " int_(1)^(2) f(x) dx is equal to

If f'(x) = f(x)+ int _(0)^(1)f (x) dx and given f (0) =1, then int f (x) dx is equal to :

Let f(x) = (alpha x^(2))/(x + 1), x ne - 1 , The value of alpha for which f(a) = a , (a ne 0 ) is

If f(x) = (1)/(2x-1) , x ne (1)/(2) , then show that : f(f(x)) = (2x-1)/(3-2x) , x ne (3)/(2)

Let f(x) =inte^x(x-1)(x-2)dx, then f(x) decrease in the interval

If a f(x)+b f((1)/(x))=(1)/(x)-5,x ne 0,a ne b , then int_1^2 f(x)dx equals

Let the function f be defined by f (x) = |x-1| -1/2, 0 le x le 2, f (x +2 ) = f (x) for all x in R. Evaluate (i) int _(0) ^(100) f (x) dx (ii) int _(0) ^(1)| f(2x ) |dx