Advertisements
Advertisements
प्रश्न
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Advertisements
उत्तर
`int(2)/(sqrt(x) - sqrt(x + 3)).dx = int (2)/(sqrt(x) - sqrt(x + 3)) xx (sqrt(x) + sqrt(x + 3))/(sqrt(x) + sqrt(x + 3)).dx`
= `int(2(sqrt(x) + sqrt(x + 3)))/(x - (x + 3)).dx`
= `-(2)/(3) int(sqrt(x) + sqrt(x + 3)).dx`
= `-(2)/(3) int x^(1/2) dx - (2)/(3) int(x + 3)^(1/2).dx`
= `-(2)/(3).(x^(3/2))/((3/2)) - (2)/(3).((x + 3)^(3/2))/((3/2)) + c`
= `-(4)/(9)[x^(3/2) + (x + 3)^(3/2)] + c`
संबंधित प्रश्न
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`(1+ log x)^2/x`
Write a value of
Write a value of
Write a value of
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int 1/("x" log "x")`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`
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate: ∫ |x| dx if x < 0
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int (cos2x)/(sin^2x) "d"x`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int (f^'(x))/(f(x))dx` = ______ + c.
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 ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
`int (logx)^2/x dx` = ______.
`int secx/(secx - tanx)dx` equals ______.
Find : `int sqrt(x/(1 - x^3))dx; x ∈ (0, 1)`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate `int(1 + x + x^2/(2!))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).
`int (cos4x)/(sin2x + cos2x)dx` = ______.
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
