Advertisements
Advertisements
प्रश्न
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Advertisements
उत्तर
`int (cos2x)/(sin^2x.cos^2x)dx`
= `int(cos^2x - sin^2x)/(sin^2x.cos^2x)dx`
= `int(1/sin^2x - 1/cos^2x)dx`
= `int "cosec"^2x dx - int sec^2 x dx`
= – cot x – tan x + c.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`1/(1 - tan x)`
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `sin(x - a)/cos(x + b)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int sqrt((10 + x)/(10 - x)).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/(sqrt(3"x"^2 + 8))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate `int (5"x" + 1)^(4/9)` dx
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
`int (7x + 9)^13 "d"x` ______ + c
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
