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
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
Write a value of
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: ∫ |x| dx if x < 0
`int (sin4x)/(cos 2x) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int_1^3 ("d"x)/(x(1 + logx)^2)` = ______.
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
`int x^3 e^(x^2) dx`
`int "cosec"^4x dx` = ______.
Evaluate:
`int sin^2(x/2)dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Which standard substitution is used for \[\sqrt{x^2-a^2}\], \[\frac{1}{\sqrt{x^2-a^2}}\], or \[x^2-a^2\]?
Which substitution is appropriate for \[\sqrt{\frac{x}{x-a}}\], \[\sqrt{\frac{x-a}{x}}\], \[\sqrt{x(x-\mathrm{a})}\], or \[\frac{1}{\sqrt{x(x-\mathrm{a})}}\]?
What is \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
