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
Find: `int(x+3)sqrt(3-4x-x^2dx)`
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals:
`int x/(x + 2).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate:
`int (5x^2 - 6x + 3)/(2x − 3)` dx
Evaluate: `int log ("x"^2 + "x")` dx
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int(1 - x)^(-2) dx` = ______.
`int (cos x)/(1 - sin x) "dx" =` ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
Write `int cotx dx`.
`int (logx)^2/x dx` = ______.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int1/(x^2+4x-5) dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`int(cos 2x)/sinx dx`
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
For \[t=\cos x\], what is \[dt\]?
