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 : `int (sinx)/sqrt(36-cos^2x)dx`
Evaluate :`intxlogxdx`
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`x/(e^(x^2))`
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Choose the correct option from the given alternatives :
`int (1 + x + sqrt(x + x^2))/(sqrt(x) + sqrt(1 + x))*dx` =
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
`int logx/x "d"x`
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intxsqrt(1+x^2)dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
