Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Advertisements
उत्तर
Let I = `int (1)/sqrt(8 - 3x + 2x^2).dx`
I = `int (1)/sqrt(2x^2 - 3x + 8).dx`
I = `1/sqrt2 int 1/sqrt(x^2 - 3/2x + 4)dx`
I = `1/sqrt2 int 1/sqrt((x^2 - 3/2x + 9/16) + 4 -9/16)dx`
I = `1/sqrt2 int 1/sqrt((x - 3/4)^2 + (sqrt(55)/4)^2`
I = `(1)/sqrt(2) log| x - (3)/(4) + sqrt((x - (3)/(4))^2 + (55/4)^2)|`
I =`(1)/sqrt(2) log| x - (3)/(4) + sqrt(x^2 - (3x)/(2) + 4)| + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`(e^(2x) - 1)/(e^(2x) + 1)`
Integrate the functions:
cot x log sin x
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Write a value of
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (cos2x)/(sin^2x) "d"x`
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`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` = ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
What is \[\int\cot t\,dt\] in the evaluation of \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
