Advertisements
Advertisements
Question
Integrate the following with respect to x:
x sec x tan x
Advertisements
Solution
`int x sec x tan x "d"x`
u = x
u’ = 1
u” = 0
dv = sec x tan x dx
v = `int sec x tan x "d"x` = sec x
v1 = `int "v" "d"x`
= `int sec x "d"x`
= `log |sec x + tan x|`
v2 = `int "v"_1 "d"x`
= `int log |sec x + tan x| "d"x`
`int "u" "dv"` = uv – u’v1 + u”v2 – u”’v3 + ………….
`int x sec x tan x "d"x = x sec x – 1 × log |sec x + tan x| + 0 xx int log |x sec x tan x| + "c"`
`int x sec x tan x "d"x = x sec x – log |sec x + tan x| + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
