Advertisements
Advertisements
Question
Integrate the following with respect to x :
x(1 – x)17
Advertisements
Solution
`int x(1 - x)^17 "d"x`
Put 1 – x = u
– dx = du
`int x(1 - x)^17 "d"x = int (1 - "u")"u"^17 xx - "du"`
= `- int ("u"^17 - "u"^18) "du"`
= `- int "u"^17 "du" + int "u"^18 "du"`
= `- ("u"^(17 + 1))/(17 + 1) + ("u"^(18 + 1))/(18 + 1) + "c"`
= `- "u"^18/18 + "u"^19/19 + "c"`
= `- (1 - x)^18/18 + (1 - x)^19/19 + "c"`
`int x(1 - x)^17 "d"x = (1 - x)^19/19 - (1 - x)^18/18 + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int1/(x(3+logx))dx`
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Evaluate : `int _0^1 ("x" . ("sin"^-1 "x")^2)/sqrt (1 - "x"^2)` dx
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
x sec x tan 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:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
