Home
Class 12
MATHS
If int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1...

If `int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1)+B F(x-4)+Ca n dF(x)=int(e^x)/xdx ,t h e n` `A=-2/3` (b) `b=(4/3)e^3` `A=2/3` (d) `d in R`

A

`A= -2//3`

B

`B=(4//3)e^(3)`

C

`A=2//3`

D

`B=(8//3)e^(3)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`(2x)/((x-1)(x-4))=(C)/(x-1)+(D)/(x-4)`
`2x=C(x-4)+D(x-1)`
` :. C= -2//3, D=8//3`
` :. int(e^(x-1))/((x^(2)-5x+4))2xdx=int e^(x-1)((-2//3)/(x-1)+(8//3)/(x-4))dx`
`= -(2)/(3)F(x-1)+(8)/(3)e^(3)F(x-4)+C`
` :. A= -2//3, B=8//3e^(3)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Single)|77 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

If int f' (x) e^(x^(2)) dx = (x-1)e^(x^(2)) + c , then f (x) is

If int (4e^x+6e^-x)/(9e^x-4e^-x)dx=Ax+B ln (9e^(2x)-4)+C , then

If int f'(x) e^(x^(2))dx = (x-1)e^(x^(2))+c then f (x) is . . . . .

x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn= 1 b. 2 c. 3 d. 4

Ifint(3e^x-5e^(-1))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n

Evaluate: int (e^x - 1)^(2) e^(-4x) dx .

If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x)=2x (d) g(x)=x

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d) none of these

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c ,t h e n f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1) f(x) has two points of extrema