Advertisements
Advertisements
Question
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Advertisements
Solution
Let I = `int "dx"/(3 - 2"x" - "x"^2)`
3 - 2x - x2 = - x2 - 2x + 3
= -(x2 + 2x - 3)
= - (x2 + 2x + 1 - 4)
= - [(x + 1)2 - 4]
= (2)2 - (x + 1)2
∴ I = `int "dx"/((2)^2 - ("x + 1")^2)`
`= 1/(2(2)) log |(2 + "x" + 1)/(2 - ("x + 1"))|` + c
∴ I = `1/4 log |(3 + "x")/(1 - "x")|` + c
APPEARS IN
RELATED QUESTIONS
Integrate the function in `((x- 3)e^x)/(x - 1)^3`.
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Evaluate the following : `int(sin(logx)^2)/x.log.x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
∫ x log x dx
`int cot "x".log [log (sin "x")] "dx"` = ____________.
Find `int_0^1 x(tan^-1x) "d"x`
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
`int_0^1 x tan^-1 x dx` = ______.
`int(1-x)^-2 dx` = ______
Evaluate:
`int(1+logx)/(x(3+logx)(2+3logx)) dx`
Evaluate:
`int (sin(x - a))/(sin(x + a))dx`
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
Evaluate the following.
`intx^3e^(x^2) dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate the following.
`intx^2e^(4x)dx`
The value of `inta^x.e^x dx` equals
Evaluate `int(1 + x + x^2/(2!))dx`.
