Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Advertisements
उत्तर
`int "e"^("a"x) cos "b"x "d"x = "e"^("a"x)/("a"^2 + "b"^2) ["a" cos "b"x + "b" sin "b"x] + "c"`
Here a = – 3, b = 1
`int "e"^(- 3x) cos x "d"x = "e"^(- 3x)/((- 3)^2 + 1^2) [- 3 cos x + 1 sin x] + "c"`
`int "e"^(- 3x) cos x "d"x = "e"^(- 3x)/(9 + 1) [sin x - 3 cos x] + "c"`
`int "e"^(- 3x) cos x "d"x = "e"^(- 3x)/10 [sin x - 3 cos 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
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Choose the correct alternative:
If `int 3^(1/x)/x^2 "d"x = "k"(3^(1/x)) + "c"`, then the value of k is
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
