Advertisements
Advertisements
Question
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Advertisements
Solution
`int ("d"x)/sqrt((2 + x)^2 - 1) = int ("d"x)/sqrt((2 + x)^2 - 1^2)`
Put 2 + x = t
dx = dt
`int ("d"x)/sqrt((2 + x)^2 - 1) = int ("d"x)/sqrt("t"^2 - 1^2)`
`int ("d"x)/sqrt(x^2 - "a"^2) = log|x + sqrt(x^2 - "a"^2)| + "c"`
= `log |"t" + sqrt("t"^2 - 1^2)| + "c"``int ("d"x)/sqrt((2 + x)^2 - 1) = log |(2 + x) + sqrt((2 + x)^2 - 1)| + "c"`
APPEARS IN
RELATED QUESTIONS
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Evaluate:`int(tansqrtx)/sqrtxdx`
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/(25 - 4x^2)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
