Advertisements
Advertisements
प्रश्न
`int 1/sqrt(x^2 - 8x - 20) "d"x`
Advertisements
उत्तर
Let I = `int 1/sqrt(x^2 - 8x - 20) "d"x`
= `int 1/sqrt(x^2 - 2.4x + 16 - 16 - 20) "d"x`
= `int ("d"x)/sqrt((x - 4)^2 - 36) "d"x`
= `int ("d"x)/sqrt((x - 4)^2 - 6^2) "d"x`
= `log|(x - 4) + sqrt((x - 4)^2 - 6^2)| + "c"`
∴ I = `log|(x - 4) + sqrt(x^2 - 8x - 20)| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the function in (sin-1x)2.
Integrate the function in ex (sinx + cosx).
Integrate the function in e2x sin x.
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int cos sqrt(x).dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Integrate the following w.r.t.x : log (x2 + 1)
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate: `int "dx"/("9x"^2 - 25)`
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int sin4x cos3x "d"x`
`int sqrt(tanx) + sqrt(cotx) "d"x`
`int 1/x "d"x` = ______ + c
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int 1/(4x^2 - 1) "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int(logx)^2dx` equals ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
`int(1-x)^-2 dx` = ______
Evaluate:
`int (logx)^2 dx`
If u and v are two differentiable functions of x, then prove that `intu*v*dx = u*intv dx - int(d/dx u)(intv dx)dx`. Hence evaluate: `intx cos x dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
