Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x:
`"e"^(2x) sinx`
Advertisements
उत्तर
`int "e"^(2x) sin"b"x "d"x = "e"^("a"x)/("a"^2 + "b"^2) ["a" sin "b"x - "b" cos "b"x] + "c"`
Here a = 2, b = 1
∴ `int "e"^(2x) sin x "d"x = "e"^(2x)/(2^2 + 1^2) [2 sin x - cos x] + "c"`
`int "e"^(2x) sin x "d"x = "e"^(x)/(4 + 1) [2 sin x - cos x] + "c"`
`int "e"^(2x) sin x "d"x = "e"^(2x)/5 [2 sin x - cos x] + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(sin^-1 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 sec x tan x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
