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
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Evaluate `int (x-1)/(sqrt(x^2 - x)) dx`
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of\[\int\frac{\sin 2x}{a^2 \sin^2 x + b^2 \cos^2 x} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(x^n - 1)/sqrt(1 + 4x^n)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
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
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int 1/(cos x - sin x)` dx = _______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`int(cos 2x)/sinx dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
