Advertisements
Advertisements
प्रश्न
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Advertisements
उत्तर
Let `I = int (cos x - sin x)/ (1 + sin 2x) dx`
`= int (cos x - sin x)/(1 + 2 sinx cosx) dx` .... [∵ sin2x = 2sinx cosx]
`= int (cosx - sin x)/(sin^2x + cos^2x + 2 sin x cos x) dx`
`= int (cos x - sin x)/ (cos x + sinx)^2 dx`
Put cos x + sin x = t
⇒ (- sin x + cos x) dx = dt
∴ `I = intdt/t^2 = t^(-2+1)/(-2 + 1) + C`
`= (-1)/t + C`
`= -1/ (cos x + sin x) + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
`(sin^2 x)/(1 + cos x)`
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
tan3 2x sec 2x
Find the integrals of the function:
tan4x
Find the integrals of the function:
`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
sin−1 (cos x)
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Evaluate `int_0^(3/2) |x sin pix|dx`
Find `int((3 sin x - 2) cos x)/(13 - cos^2 x- 7 sin x) dx`
Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (log "x")^2 d"x"`
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Find `int "dx"/(2sin^2x + 5cos^2x)`
Find `int x^2tan^-1x"d"x`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int ("d"x)/(1 + cos x)`
Evaluate the following:
`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
Evaluate the following:
`int (cosx - cos2x)/(1 - cosx) "d"x`
Evaluate the following:
`int "e"^(tan^-1x) ((1 + x + x^2)/(1 + x^2)) "d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.
`int sinx/(3 + 4cos^2x) "d"x` = ______.
