Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/("x"^2 + 4"x" - 5)` dx
Advertisements
उत्तर
Let I = `int 1/("x"^2 + 4"x" - 5)` dx
`= int 1/("x"^2 + 4"x" + 4 - 4 - 5)` dx
`= int 1/(("x + 2")^2 - 9) "dx"`
`= int 1/(("x" + 2)^2 - 3^2)` dx
`= 1/(2 xx 3) log |(("x" + 2) - 3)/(("x" + 2) + 3)|` + c
∴ I = `1/6 log |("x" - 1)/("x" + 5)|` + c
APPEARS IN
संबंधित प्रश्न
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : tan5x
Evaluate the following:
`int sinx/(sin 3x) dx`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int (log x)/(log ex)^2` dx = _________
`int cos^7 x "d"x`
`int sec^6 x tan x "d"x` = ______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int (1+x+x^2/(2!))dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
