Advertisements
Advertisements
Question
`int (dx)/(sin^2 x cos^2 x)` equals:
Options
tan x + cot x + C
tan x - cot x + C
tan x cot x + C
tan x - cot 2x + C
Solution
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
RELATED QUESTIONS
Integrate the functions:
`sqrt(ax + b)`
Write a value of\[\int a^x e^x \text{ dx }\]
Write a value of
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following : `int sinx/(sin 3x).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
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
`int (log x)/(log ex)^2` dx = _________
`int ("d"x)/(x(x^4 + 1))` = ______.
`int 1/(sinx.cos^2x)dx` = ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3) dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
Evaluate `int 1/(x(x-1)) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
