Advertisements
Advertisements
प्रश्न
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Advertisements
उत्तर
`int (x + 2)/sqrt(x^2 - 4x - 5) dx`
= `int (x + 2 - 2 + 2)/sqrt(x^2 - 4x - 5)dx`
= `int (x - 2)/sqrt(x^2 - 4x - 5)dx + int 4/sqrt(x^2 - 4x - 5)dx`
= `int (x - 2)/sqrt(x^2 - 4x - 5)dx + int 4/sqrt(x^2 - 4x - 5 - 4 + 4)dx`
Let x2 – 4x – 5 = u
(2x – 4) = `(du)/dx`
(x – 2) dx = `(du)/2`
= `int (du)/(2sqrt(u)) + int 4/sqrt((x - 2)^2 - (3)^2) dx`
= `1/2. sqrt(u)/(1/2) + 4 log |(x - 2) + sqrt((x - 2)^2 - (3)^2)| + C`
= `sqrt(x^2 - 4x - 5) + 4 log |x - 2 + sqrt(x^2 - 4x - 5)| + C`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Evaluate: `int 1/(x(x-1)) dx`
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
`int "dx"/(9"x"^2 + 1)= ______. `
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int sqrt(1 + sin2x) dx`
`int(log(logx))/x "d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int 1/(a^2 - x^2) dx = 1/(2a) xx` ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate the following
`int x^3/sqrt(1+x^4) dx`
Evaluate `int 1/(x(x-1))dx`
