Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Advertisements
उत्तर
`int sqrt(x^2 + 2x + 10) "d"x = int sqrt((x + 1)^2 + 1^2 + 10) "d"x`
= `int sqrt((x + 1)^2 + 9) "d"x`
= `int sqrt((x + 1)^2 + 3^2) "d"x`
Put x + 1 = t
dx = dt
= `int sqrt("t"^2 + 3^2) "dt"`
= `"t"/2 sqrt("t" + 3^2) + 3^2/2 log |"t" + sqrt("t"^2 + 3^2)| + "c"`
= `"t"/2 sqrt("t"^2 + 3^2) + 3^2/2 log |"t" + sqrt("t"^2 + 3^2)| + "c"`
= `((x + 1))/2 sqrt((x + 1)^2 + 3^2) + 3^2/2 log |x + 1 sqrt((x + 1)^2 + 9)| + "c"`
= `((x + 1))/2 sqrt(x^2 + 2x 1 + 9) + 9/2 log |x + 1 + sqrt(x^2 + 2x + 1 + 9)| + "c"`
= `((x + 1))/2 sqrt(x^2 + 2x + 10) + 9/2 log |x + 1 + sqrt(x^2 + 2x + 10)| + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate:`int(tansqrtx)/sqrtxdx`
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
Choose the correct alternative:
`int x^2 "e"^(x/2) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
