Advertisements
Advertisements
प्रश्न
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Advertisements
उत्तर
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`
संबंधित प्रश्न
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`x/(e^(x^2))`
Integrate the functions:
`1/(1 + cot x)`
Write a value of
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals : `int (3)/(sqrt(7x - 2) - sqrt(7x - 5)).dx`
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Evaluate: `int log ("x"^2 + "x")` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int(log(logx) + 1/(logx)^2)dx` = ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
`int (logx)^2/x dx` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
`int "cosec"^4x dx` = ______.
Evaluate `int 1/(x(x-1))dx`
`int x^2/sqrt(1 - x^6)dx` = ______.
`int (cos4x)/(sin2x + cos2x)dx` = ______.
