Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`"e"^x sec x(1 + tan x)`
Advertisements
उत्तर
Let I = I
= `int "e"^x (sec x + sec x tan x) "d"x`
Take f(x) = sec x
f‘(x) = sec x tan x
This is of the form of `int "e"^x ["f"(x) + "f'"(x)] "d"x = "e"^x "f"(x) + "c"`
= ex sec x + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate : `∫_0^(pi/2) (sinx.cosx)/(1 + sin^4x)`.dx
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
