Advertisements
Advertisements
Question
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Advertisements
Solution
`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
RELATED QUESTIONS
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Evaluate : `∫1/(3+2sinx+cosx)dx`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following.
`int "x"^5/("x"^2 + 1)`dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int 1/((2"x" + 3))` dx
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int (log x)/(log ex)^2` dx = _________
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int cot^2x "d"x`
`int x/(x + 2) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
