Advertisements
Advertisements
प्रश्न
`int (cos2x)/(sin^2x) "d"x`
Advertisements
उत्तर
`int (cos2x)/(sin^2x) "d"x`
= `int (1 - 2sin^2x)/(sin^2x) "d"x` ......[∵ cos 2θ = 1 − 2sin2θ]
= `int(1/(sin^2x) - (2sin^2x)/(sin^2x)) "d"x`
= `int ("cosec"^2x - 2) "d"x`
= −cot x − 2x + c
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Evaluate :
`∫(x+2)/sqrt(x^2+5x+6)dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`1/(1 - tan 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
Write a value of
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
Integrate the following functions w.r.t. x : `(3e^(2x) + 5)/(4e^(2x) - 5)`
Evaluate the following : `int (1)/sqrt(2x^2 - 5).dx`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 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 dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate: `int log ("x"^2 + "x")` dx
`int 1/(xsin^2(logx)) "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int dx/(1 + e^-x)` = ______
`int(5x + 2)/(3x - 4) dx` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int ("d"x)/(x(x^4 + 1))` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Write `int cotx dx`.
`int (logx)^2/x dx` = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?
What is \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
