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 : `int1/(x(3+logx))dx`
Find the volume of solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`1/(x log x log (log 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"^x (tan x + log sec x)`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
