Advertisements
Advertisements
प्रश्न
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
Advertisements
उत्तर
Let I = `int sqrt(x)*sec(x^(3/2))*tan(x^(3/2))"d"x`
Put `x^(3/2)` = t
∴ `3/2x^(1/2) "d"x` = dt
∴ `sqrt(x) "d"x = 2/3 "dt"`
∴ I = `2/3 int sec "t"*tan"t"* "dt"`
= `2/3 sec "t" + "c"`
∴ I = `2/3 sec(x^(3/2)) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Write a value of
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Evaluate the following integrals : `int sqrt(1 + sin 2x) dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
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 : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Integrate the following functions w.r.t.x:
cos8xcotx
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Integrate the following functions w.r.t. x : `int (1)/(2sin 2x - 3)dx`
Evaluate the following integrals:
`int (2x + 1)/(x^2 + 4x - 5).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Evaluate: `int "e"^"x" (1 + "x")/(2 + "x")^2` dx
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int logx/x "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int1/(4 + 3cos^2x)dx` = ______
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
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.
`intx sqrt(1 +x^2) dx`
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
