Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Advertisements
उत्तर
I = `int (1)/(4x^2 - 3).dx`
= `(1)/(4) int (1)/(x^2 - 3/4).dx`
= `(1)/(4) int (1)/(x^2 - (sqrt(3)/2)^2).dx`
= `(1)/(4) (1)/(2(sqrt(3)/2))log|(x - sqrt(3)/(2))/(x + sqrt(3)/(2))| + c`
= `(1)/(4sqrt(3)) log |(2x - sqrt(3))/(2x + sqrt(3))| + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
`int (log x)/(log ex)^2` dx = _________
`int (sin4x)/(cos 2x) "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int sec^6 x tan x "d"x` = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
What must be done before integrating after obtaining \[du\]?
How should a substitution be chosen?
