Advertisements
Advertisements
Question
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Advertisements
Solution
`int(2)/(sqrt(x) - sqrt(x + 3)).dx = int (2)/(sqrt(x) - sqrt(x + 3)) xx (sqrt(x) + sqrt(x + 3))/(sqrt(x) + sqrt(x + 3)).dx`
= `int(2(sqrt(x) + sqrt(x + 3)))/(x - (x + 3)).dx`
= `-(2)/(3) int(sqrt(x) + sqrt(x + 3)).dx`
= `-(2)/(3) int x^(1/2) dx - (2)/(3) int(x + 3)^(1/2).dx`
= `-(2)/(3).(x^(3/2))/((3/2)) - (2)/(3).((x + 3)^(3/2))/((3/2)) + c`
= `-(4)/(9)[x^(3/2) + (x + 3)^(3/2)] + c`
RELATED QUESTIONS
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`sin x/(1+ cos x)`
Integrate the functions:
`1/(1 - tan x)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(4 - 5cosx).dx`
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int(1 - x)^(-2) dx` = ______.
`int x^3"e"^(x^2) "d"x`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int (cos x)/(1 - sin x) "dx" =` ______.
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate `int(1+ x + x^2/(2!)) dx`
if `f(x) = 4x^3 - 3x^2 + 2x +k, f (0) = - 1 and f (1) = 4, "find " f(x)`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
What is \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
