Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Advertisements
उत्तर
`int (1)/(x^2 + 8x + 12).dx`
= `int (1)/((x^2 + 8x + 16) - 16 + 12).dx`
= `int (1)/((x + 4)^2 - 2^2).dx`
= `(1)/(2(2)) log |((x + 4) - 2)/((x + 4) + 2)| + c`
= `(1)/(4) log |(x + 2)/(x + 6)| + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int cos sqrtx` dx = _____________
`int sqrt(1 + sin2x) dx`
`int cot^2x "d"x`
`int x/(x + 2) "d"x`
`int x^3"e"^(x^2) "d"x`
`int sin^-1 x`dx = ?
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate `int 1/(x(x-1))dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
