Advertisements
Advertisements
Question
Find `int (sin^2 x - cos^2x)/(sin x cos x) dx`
Advertisements
Solution
`int (sin^2 x - cos^2x)/(sin x cos x) dx`
= `int (sin^2 x)/(sin x cos x) dx - int (cos^2 x)/(sin x cos x) dx`
= `int tan x dx - int cot x dx`
= log |sec x| - log |sin x| + C
APPEARS IN
RELATED QUESTIONS
Evaluate : `intsin(x-a)/sin(x+a)dx`
Find the integrals of the function:
sin2 (2x + 5)
Find the integrals of the function:
sin 3x cos 4x
Find the integrals of the function:
sin4 x
Find the integrals of the function:
cos4 2x
Find the integrals of the function:
`(sin^2 x)/(1 + cos x)`
Find the integrals of the function:
`1/(sin xcos^3 x)`
Evaluate: `int_0^π (x sin x)/(1 + cos^2x) dx`.
Differentiate : \[\tan^{- 1} \left( \frac{1 + \cos x}{\sin x} \right)\] with respect to x .
Evaluate : \[\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot cosec x}dx\] .
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_ (sin2"x")/((sin^2 "x"+1)(sin^2"x"+3))d"x"`
Find the area of the triangle whose vertices are (-1, 1), (0, 5) and (3, 2), using integration.
Integrate the function `cos("x + a")/sin("x + b")` w.r.t. x.
Find: `intsqrt(1 - sin 2x) dx, pi/4 < x < pi/2`
Find: `int sin^-1 (2x) dx.`
Find `int x^2tan^-1x"d"x`
`int (sin^6x)/(cos^8x) "d"x` = ______.
Evaluate the following:
`int ("d"x)/(1 + cos x)`
Evaluate the following:
`int (sinx + cosx)/sqrt(1 + sin 2x) "d"x`
Evaluate the following:
`int (sin^6x + cos^6x)/(sin^2x cos^2x) "d"x`
`int sinx/(3 + 4cos^2x) "d"x` = ______.
