Advertisements
Advertisements
Question
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Advertisements
Solution
Let I = `int x/ (sqrt( x + 4)) dx`
Put x + 4 = t
⇒ dx = dt . Also, x = t - 4
∴ `I = int (t - 4)/sqrtt dt`
`= int (t^(1/2) - 4t^ (-1/2)) dt`
`= 2/3 t^(3/2) -4 xx 2t^(1/2) + C`
`= 2/3 (x + 4)^(3/2) - 8 (x + 4)^(1/2) + C`
`= 2/3 (x + 4)^(1/2) [x + 4 - 12] + C`
`= 2/3 (x + 4)^(1/2) (x - 8) + C`
RELATED QUESTIONS
Integrate the functions:
`(2x)/(1 + x^2)`
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2 sin2x + 4cos 2x).dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
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
Evaluate `int (5"x" + 1)^(4/9)` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
Evaluate: `int "e"^sqrt"x"` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int (7x + 9)^13 "d"x` ______ + c
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
Evaluate:
`int sin^3x cos^3x dx`
Evaluate:
`int(5x^2-6x+3)/(2x-3)dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
