Advertisements
Advertisements
प्रश्न
`int (dx)/(sin^2 x cos^2 x)` equals:
विकल्प
tan x + cot x + C
tan x - cot x + C
tan x cot x + C
tan x - cot 2x + C
Advertisements
उत्तर
tan x - cot x + C
Explanation:
Let `I = int dx/(sin^2 cos^2 x)`
`= int (sin^2 x cos^2 x)/(sin^2 x cos^2 x) dx`
`= int ((sin^2 x)/(sin^2 x cos^2 x) + (cos^2 x)/(sin^2 x cos^2 x)) dx`
`= int (1/(cos^2 x) + 1/(sin^2 x)) dx`
`= int (sec^2 x + cosec^2 x) dx`
`= int sec^2 dx + int cosec^2 x dx`
= tan x - cot x + C
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t.x:
cos8xcotx
Integrate the following functions w.r.t. x : tan5x
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Evaluate the following:
`int (1)/sqrt((x - 3)(x + 2)).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
`int logx/(log ex)^2*dx` = ______.
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int 1/(xsin^2(logx)) "d"x`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
The value of `intsinx/(sinx - cosx)dx` equals ______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
`int x^3 e^(x^2) dx`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
`int "cosec"^4x dx` = ______.
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5)dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
