Advertisements
Advertisements
प्रश्न
`int secx/(secx - tanx)dx` equals ______.
विकल्प
sec x – tan x + c
sec x + tan x + c
tan x + sec x + c
– (sec x + tan x) + c
Advertisements
उत्तर
`int secx/(secx - tanx)dx` equals tan x + sec x + c.
Explanation:
`int secx/(secx - tanx)dx = int (1/cosx)/(1/cosx - sinx/cosx)dx`
= `int dx/(1 - sin x)`
= `int 1/(1 - sinx) xx (1 + sin x)/(1 + sin x)dx`
= `int (1 + sinx)/(cos^2x)dx`
= `int sec^2 x dx + int tan x sec x dx`
= tan x + sec x + c.
APPEARS IN
संबंधित प्रश्न
Evaluate :`intxlogxdx`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`cos sqrt(x)/sqrtx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of\[\int\sqrt{4 - x^2} \text{ dx }\]
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int dx/(1 + e^-x)` = ______
`int (cos x)/(1 - sin x) "dx" =` ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
