Advertisements
Advertisements
प्रश्न
`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.
पर्याय
log |1 + cosx| + C
log |x + sinx| + C
`x - tan x/2 + "C"`
`x.tan x/2 + "C"`
Advertisements
उत्तर
`int (x + sinx)/(1 + cosx) "d"x` is equal to `x.tan x/2 + "C"`.
Explanation:
I = `int (x + sinx)/(1 + cosx) "d"x`
= `int x/(1 + cos x) "d"x + int (sinx)/(1 + cosx) "d"x`
= `int x/(2cos^2 x/2) "d"x + int (2sin x/2 cos x/2)/(2cos^2 x/2) "d"x`
= `int x sec^2 x/2 "d"x + int tan x/2 "d"x`
= `1/2 [x*2 tan x/2 - int 2 tan x/2 "d"x] + int tan x/2 "d"x`
= `x * tan x/2 + "C"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin 3x cos 4x
Find the integrals of the function:
cos 2x cos 4x cos 6x
Find the integrals of the function:
sin3 x cos3 x
Find the integrals of the function:
sin x sin 2x sin 3x
Find the integrals of the function:
sin 4x sin 8x
Find the integrals of the function:
sin4 x
Find the integrals of the function:
cos4 2x
Find the integrals of the function:
`(sin^2 x)/(1 + cos x)`
Find the integrals of the function:
`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
`(cos 2x+ 2sin^2x)/(cos^2 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 ______.
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Evaluate `int_0^(3/2) |x sin pix|dx`
Find `int (2x)/((x^2 + 1)(x^4 + 4))`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 .
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Find:
`int"dx"/sqrt(5-4"x" - 2"x"^2)`
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Find: `int sin^-1 (2x) dx.`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int "dx"/(2sin^2x + 5cos^2x)`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
Evaluate the following:
`int sin^-1 sqrt(x/("a" + x)) "d"x` (Hint: Put x = a tan2θ)
`int sinx/(3 + 4cos^2x) "d"x` = ______.
`int (cos^2x)/(sin x + cos x)^2 dx` is equal to
