Advertisements
Advertisements
Question
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Solution
`int ("d"x)/((x + 1)^2 - 25)`
Put x + 1 = t
dx = dt
`int "dt"/((x + 1)^2 - 5^2) = int "dt"/("t"^2 - 5^2)`
`int ("d"x)/(x^2 - "a"^2) = 1/(2"a") log |(x - "a")/(x + "a")| + "c"`
= `1/(2 xx 5) log |("t" - 5)/("t" + 5)| + "c"`
= `1/10 log |("t" - 5)/("t" + 5)| + "c"`
= `1/10 log |(x + 1 - 5)/(x + 1 + 5)| + "c"`
`int ("d"x)/((x + 1)^2 - 25) = 1/10 log |(x - 4)/(x + 6)| + "c"`
APPEARS IN
RELATED QUESTIONS
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.
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following with respect to x :
`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
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 sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
