Advertisements
Advertisements
Question
Integrate the following with respect to x:
x sin 3x
Advertisements
Solution
`int x sin 3x "d"x`
`int "u" "dv" = "uv" - "u""'""v"_1 + "u""'""v"_2 - "u""'""v"_3 +` ..........(1)
u = x
u' = 1
u" = 0
v1 = `int "v" "d"x``
= `int - (cos 3x)/3`
= `- 1/3 xx (sin 3x)/3`
v2 = `int "v"_1 "d"x`
= `int - 1/3^2 sin3x * "d"x`
= `- 1/3^2 xx 1/3 xx - cos 3x`
= `1/3^2 cos 3x`
`int x sin x "d"x = x xx - (cos3x)/3 - 1 xx - 1/3^2 sin 3x + 0 xx 1/3^3 cos3x + "c"`
`int x sin 3x "d"x = - x/3 cos 3x + 1/9 sin 3x + "c"`
APPEARS IN
RELATED QUESTIONS
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 :
`(sin4x)/sinx`
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^3/((x - 1)(x - 2))`
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 :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
9xe3x
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:
`(3x + 1)/(2x^2 - 2x + 3)`
Choose the correct alternative:
`int "e"^(- 4x) cos "d"x` is
Choose the correct alternative:
`int (sec^2x)/(tan^2 x - 1) "d"x`
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
