Advertisements
Advertisements
Question
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Advertisements
Solution
Let I = `int "dx"/(4"x"^2 - 1)`
`= 1/4 int "dx"/("x"^2 - 1/4)`
`= 1/4 int "dx"/("x"^2 - (1/2)^2)`
`= 1/4 xx 1/(2 xx 1/2) log |("x" - 1/2)/("x" + 1/2)|` + c
∴ I = `1/4` log `|("2x" - 1)/("2x" + 1)|` + c
Alternate Method:
Let I = `int "dx"/(4"x"^2 - 1) = int "dx"/((2"x"^2) - (1)^2)`
`= 1/(2 xx 1) xx 1/2 log |("2x" - 1)/("2x" + 1)|` + c
∴ I = `1/4` log `|("2x" - 1)/("2x" + 1)|` + c
APPEARS IN
RELATED QUESTIONS
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Write a value of
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
`int 1/(cos x - sin x)` dx = _______________
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
`int secx/(secx - tanx)dx` equals ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int 1/(x(x-1)) dx`
