Advertisements
Advertisements
प्रश्न
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
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 functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
