Advertisements
Advertisements
Question
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Solution
`int "e"^(x log "a") "e"^x = int "e"^(log "a"^x) * "e"^x * "d"x`
= `int "a"^x "e"^x * "d"x`
= `int ("ae")^x * "d"x`
`[int "a"^x * "d"x = "a"^x/log"a" + "c"]`
= `("ae")^x/(log("ae")) + "c"`
APPEARS IN
RELATED QUESTIONS
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^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 sin sqrt(x) "d"x` is
