Advertisements
Advertisements
प्रश्न
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Advertisements
उत्तर
`int (1)/sqrt(2x^2 - 5).dx`
= `(1)/sqrt(2) int (1)/sqrt(x^2 - 5/2).dx`
= `(1)/sqrt(2) int (1)/sqrt(x^2 - (sqrt(5/2))^2).dx`
= `(1)/sqrt(2) log|x + sqrt(x^2 - 5/2)| + c`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`(sin^(-1) x)/(sqrt(1-x^2))`
Integrate the functions:
`(1+ log x)^2/x`
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\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int "x - 1"/sqrt("x + 4")` dx
`int (log x)/(log ex)^2` dx = _________
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
`int x^3 e^(x^2) dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
