Advertisements
Advertisements
प्रश्न
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
cot x log sin x
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Write a value of
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 1/(xsin^2(logx)) "d"x`
`int (f^'(x))/(f(x))dx` = ______ + c.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate `int 1/("x"("x" - 1)) "dx"`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx sqrt(1 +x^2) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int(1+x+x^2/(2!))dx`
