Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Advertisements
उत्तर
`int sqrt(81 + (2x + 1)^2) "d"x = int sqrt(9^2 + (2x + 1)^2) "d"x`
Put 2x + 1 = t
2 dx = dt
= `int sqrt(9^2 + "t"^2) * 1/2 "dt"`
= `1/2 int sqrt(9^2 + "t"^2) "dt"`
= `1/2 ["t"/2 sqrt("t"^2 + 9^2) + 9^2/2 log |"t" + sqrt("t" + 9^2)|] + "c"`
= `- 1/4 [(2x + 1) sqrt((2x + 1)^2 + 9^2) + 81 log |(2x + 1) + sqrt((2x + 1)^2 + 9^2)|] + "c"`
`int sqrt(81 + (2x + 1)^2) "d"x = 1/4[(2x + 1) sqrt((2x + 1)^2 + 81) + 81 log |(2x + 1) + sqrt((2x + 1)^2 + 81)|] + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
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 :
(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 :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Find the integrals of the following:
`1/(25 - 4x^2)`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
