Advertisements
Advertisements
प्रश्न
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
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_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
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 : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int(1 + x + x^2/(2!) )dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int (1)/(x(x - 1))dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
