Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x :
`tan x sqrt(sec x)`
उत्तर
`int tan x sqrt(sec x) "d"x = int sinx/cosx * sqrt(sec x) * "d"x`
= `int sin x * sec x sqrt(secx) * "d"x`
= `int sin x * (sec x)^(3/2) * "d"x`
= `int sinx/(cos x)^(3/2) * "d"x`
Put cos x = u
– sin x dx = du
sin x dx = – du
`int tan x sqrt(sec x) "d"x = int (- "du")/"u"^(3/2)`
= `- int "u"^(- 3/2) "du"`
= ` - ("u"^(- 3/2 + 1))/(- 3/2 + 1) + "c"`
= `- ("u"^(- 1/2))/(- 1/2) + "c"`
= `2 "u"^(- 1/2) + "c"`
= `2(cos x)^(- 1/2) + "c"`
= `2 1/(cos x)^(1/2) + "c"`
= `2(sec x)^(1/2) + "c"`
`int tan x sqrt(sec x) "d"x = 2 sqrt(sec x) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1) "d"x` is
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
