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
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`tan x sqrt(sec 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) sin 2x`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^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:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
