Advertisements
Advertisements
प्रश्न
Find the integrals of the following:
`1/(25 - 4x^2)`
Advertisements
उत्तर
`int 1/(25 - 4x^2) "d"x = int 1/(4(25/4 - x^2)) "d"x`
= `1/4 int ("d"x)/((5/4)^2 - x^2)`
`int ("d"x)/("a"^2 - x^2) = 1/(2"a") log |("a" + x)/("a" - x)| + "c"`
= `1/4 xx 1/(2 xx (5/2)) log |(5/2 + x)/(5/2 - x)| + "c"`
= `1/4 xx 1/5 log |((5 + 2x)/2)/((5 - 2x)/2)| + "c"`
= `1/20 log |(5 + 2x)/(5 - 2x)| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
sin2 5x
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
Choose the correct alternative:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve is
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
