Advertisements
Advertisements
Question
`int (x + sinx)/(1 + cosx) "d"x` is equal to ______.
Options
log |1 + cosx| + C
log |x + sinx| + C
`x - tan x/2 + "C"`
`x.tan x/2 + "C"`
Advertisements
Solution
`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
RELATED QUESTIONS
Find the integrals of the function:
sin 3x cos 4x
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:
`(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:
`1/(sin xcos^3 x)`
Find the integrals of the function:
sin−1 (cos x)
Find `int dx/(x^2 + 4x + 8)`
Evaluate `int_0^(3/2) |x sin pix|dx`
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (log "x")^2 d"x"`
Find `int_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))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: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Find `int x^2tan^-1x"d"x`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
`int "dx"/(sin^2x cos^2x)` is equal to ______.
Evaluate the following:
`int ((1 + cosx))/(x + sinx) "d"x`
Evaluate the following:
`int tan^2x sec^4 x"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 (cosx - cos2x)/(1 - cosx) "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` = ______.
The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4 dx` is
