Advertisements
Advertisements
प्रश्न
`int sinx/(3 + 4cos^2x) "d"x` = ______.
Advertisements
उत्तर
`int sinx/(3 + 4cos^2x) "d"x` = `- 1/(2sqrt(3)) tan^-1 (2/sqrt(3) cos x) + "C"`.
Explanation:
Let I = `int sinx/(3 + 4cos^2x) "d"x`
Put cos x = t
∴ – sin x dx = dt
⇒ sinx dx = – dt
∴ I = `- int "dt"/(3 + 4"t"^2)`
= `- 1/4 int "dt"/(3/4 + "t"^2)`
= `- 1/4 int "dt"/((sqrt(3)/2)^2 + "t"^2)`
= `1/4 xx 1/(sqrt(3)/2) tan^-1 ("t"/(sqrt(3)/2)) + "C"`
= ` 1/(2sqrt(3)) tan^-1 ((2"t")/sqrt(3)) + "C"`
= `- 1/(2sqrt(3)) tan^-1 ((2cosx)/sqrt(3)) + "C"`
Hence I = `- 1/(2sqrt(3)) tan^-1 (2/sqrt(3) cos x) + "C"`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
sin3 x cos3 x
Find the integrals of the function:
sin 4x sin 8x
Find the integrals of the function:
`(1-cosx)/(1 + cos x)`
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Find the integrals of the function:
`1/(sin xcos^3 x)`
Find the integrals of the function:
`(cos 2x)/(cos x + sin x)^2`
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`int (sin^2x - cos^2 x)/(sin^2 x cos^2 x) dx` is equal to ______.
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Find `int (2x)/((x^2 + 1)(x^4 + 4))`dx
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
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"dx"/sqrt(5-4"x" - 2"x"^2)`
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `int sec^2 x /sqrt(tan^2 x+4) dx.`
Find: `int sin^-1 (2x) dx.`
Find `int "dx"/(2sin^2x + 5cos^2x)`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int sqrt(1 + sinx)"d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "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 ______.
The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4 dx` is
