Advertisements
Advertisements
Question
Integrate the following with respect to x:
x2 cos x
Advertisements
Solution
`int x^2 cos x "d"x`
u = x2
u' = 2x
u' = 2
u"' 0
dv = cos x dx
⇒ v= `int cos x "d"x`
= sin x
v1 = `int "v" "d"x`
= `int sinx "d"x`
= `- cos x`
v2 = `int "v"_1 "d"x`
= `int - cosx "d"x`
= `- sin x`
v3 = `int "v"_2 "d"x`
= `int- sin x "d"x`
= `- int sinx "d"x`
= `- (cos x)`
`int "u" "dv"` = uv – u'v1 + uv2 – u"'v3 + ...........
`int x^2 cos x "d"x = x^2 sin x - 2x xx cos x + 2 xx - sin x - 0 xx cos x + "c"`
`int x^2 cos x "d"x = x^2 sin x + 2x cosx - 2 sinx + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int1/(x(3+logx))dx`
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 :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Integrate the following with respect to x:
`"e"^x sec x(1 + tan x)`
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Find the integrals of the following:
`1/(25 - 4x^2)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int x^2 cos x "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
