Advertisements
Advertisements
Question
`int "dx"/(sin^2x cos^2x)` is equal to ______.
Options
tanx + cotx + C
x + cotx)2 + C
tanx – cotx + C
(tanx – cotx)2 + C
Advertisements
Solution
`int "dx"/(sin^2x cos^2x)` is equal to tanx – cotx + C.
Explanation:
I = `int ("d"x)/(sin^2x cos^2x)`
= `int ((sin^2x + cos^2x)"d"x)/(sin^2xcos^2x)`
= `int sec^2 x"d"x + int "cosec"^2x "d"x`
= tanx – cotx + C
APPEARS IN
RELATED QUESTIONS
Evaluate :`int_(pi/6)^(pi/3) dx/(1+sqrtcotx)`
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
cos 2x cos 4x cos 6x
Find the integrals of the function:
sin3 (2x + 1)
Find the integrals of the function:
sin3 x cos3 x
Find the integrals of the function:
`(1-cosx)/(1 + cos x)`
Find the integrals of the function:
`(sin^2 x)/(1 + cos x)`
Find the integrals of the function:
`(cos 2x - cos 2 alpha)/(cos x - cos alpha)`
Find the integrals of the function:
`(cos x - sinx)/(1+sin 2x)`
Find the integrals of the function:
`(sin^3 x + cos^3 x)/(sin^2x cos^2 x)`
Find the integrals of the function:
`1/(sin xcos^3 x)`
Find the integrals of the function:
sin−1 (cos x)
Find the integrals of the function:
`1/(cos(x - a) cos(x - b))`
`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.
Find `int_ (sin "x" - cos "x" )/sqrt(1 + sin 2"x") d"x", 0 < "x" < π / 2 `
Find `int_ sin ("x" - a)/(sin ("x" + a )) d"x"`
Find `int_ (log "x")^2 d"x"`
Find: `int_ (cos"x")/((1 + sin "x") (2+ sin"x")) "dx"`
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Evaluate `int tan^8 x sec^4 x"d"x`
Find `int "dx"/(2sin^2x + 5cos^2x)`
Find `int x^2tan^-1x"d"x`
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
Evaluate the following:
`int tan^2x sec^4 x"d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
The value of the integral `int_(1/3)^1 (x - x^3)^(1/3)/x^4 dx` is
What does integration using trigonometric identities mean?
What is \(\int \cos^2 x\,dx\)?
What should be done first when evaluating an integral containing a complicated trigonometric expression?
What must always be added to an indefinite integral?
