Advertisements
Advertisements
Question
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Advertisements
Solution
`int (1)/(4x^2 - 20x + 17).dx`
= `(1)/(4) int (1)/(x^2 - 5x + 17/4).dx`
= `(1)/(4) int (1)/((x^2 - 5x + 25/4) - (25)/(4) + (17)/(4)).dx`
= `(1)/(4) int (1)/((x - 5/2)^2 - (sqrt(2))^2).dx`
= `(1)/(4) xx (1)/(2sqrt(2))log|(x - 5/2 - sqrt(2))/(x - 5/2 + sqrt(2))| + c`
= `(1)/(8sqrt(2))log |(2x - 5 - 2sqrt(2))/(2x - 5 + 2sqrt(2))| + c`.
APPEARS IN
RELATED QUESTIONS
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Evaluate: `int 1/(x(x-1)) dx`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of\[\int \log_e x\ dx\].
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
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 = _______
`int x^2/sqrt(1 - x^6)` dx = ________________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int x^3"e"^(x^2) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int sin^-1 x`dx = ?
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int (cos x)/(1 - sin x) "dx" =` ______.
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int(log(logx) + 1/(logx)^2)dx` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
