Advertisements
Advertisements
Question
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Solution
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
RELATED QUESTIONS
Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Evaluate :
`int1/(sin^4x+sin^2xcos^2x+cos^4x)dx`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`e^(2x+3)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Evaluate the following integrals : `int cos^2x.dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).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 : sin4x.cos3x
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x:
`(10x^9 10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Integrate the following w.r.t.x : `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Evaluate: `int "x" * "e"^"2x"` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int sqrt(x^2 + 2x + 5)` dx = ______________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int x/(x + 2) "d"x`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int dx/(1 + e^-x)` = ______
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`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(log(logx) + 1/(logx)^2)dx` = ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate `int1/(x(x - 1))dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int (1)/(x(x - 1))dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int 1/(x(x-1))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
